Bio papers — 2026-10-22

The Morning Preprint — this day as one edition: the day's papers, the five things worth knowing, and the episodes behind them.

This work addresses how to make protein-ligand docking more accurate when both molecules can move flexibly. This is important because most current diffusion models do not account for the periodic nature of angular variables in torsional motions.

The key research is Harmony, a harmonic torsional diffusion framework designed for this flexible docking challenge. This method introduces learned harmonic potentials on the circle to parameterize ligand and side-chain torsional score fields. These fields are then noised mode by mode in the Fourier basis due to variance-exploding diffusion on the torus.

This construction makes periodicity apparent and provides a frequency-aware inductive bias over rotameric motion. This improved modeling capability leads to better performance on established benchmarks, such as the PDBBind benchmark AKMPC. Harmony improves both ligand pose accuracy and pocket all-atom reconstruction when tested on this benchmark AKMPC.

Furthermore, it enhances the physical validity of generated complexes as shown in PoseBusters AKMPC. Case studies on EBNA1 and KRAS G12D demonstrate how this approach handles different types of binding sites, such as polar and shallow ones. Overall, these findings suggest that aligning the score parameterization with the geometry of the diffusion process is a simple yet effective way to boost flexible docking accuracy.

Today's papers

• Harmonic Torsional Diffusion for Protein-Ligand Flexible Docking Harmony introduces a new method that explicitly handles the periodic nature of rotational movements in protein-ligand docking by using harmonic potentials on the circle. This approach improves docking accuracy and physical realism when dealing with flexible proteins and ligands. This method makes the score parameterization match the geometry of how diffusion updates occur, which helps improve flexible docking performance. Harmony is a harmonic torsional diffusion framework designed to better model the complex conformational changes in protein-ligand binding. The paper shows that aligning the scoring function with periodic geometry significantly enhances accurate prediction of ligand poses and pocket structures in flexible docking. This work demonstrates that using learned harmonic potentials on a circle, which are noise-mode by mode, provides a frequency-aware bias for rotameric motion during diffusion. Harmony is a method for flexible protein-ligand docking that uses harmonic potentials to explicitly account for the periodic nature of torsional degrees of freedom. The results show Harmony improves ligand pose accuracy and pocket reconstruction on the PDBBind benchmark and increases physical validity on PoseBusters. Case studies confirm that this method works well on both polar and shallow binding sites. This research suggests that aligning the score parameterization with the diffusion process geometry is an effective way to improve flexible docking models. The core idea of Harmony is to use harmonic potentials defined on a circle to better capture the periodic nature of torsional motion in flexible docking simulations. The paper presents Harmony as a framework that uses learned harmonic potentials on the circle, which are noise-mode by mode, to parameterize torsional score fields for flexible protein-ligand docking. This method makes periodicity explicit and gives the model an inductive bias over rotameric motion. Harmony is a method for flexible protein-ligand docking that uses harmonic potentials on the circle to explicitly handle periodic geometry in torsional updates. The results show that aligning the score parameterization with the geometry of diffusion improves flexible docking outcomes significantly. This paper introduces Harmony, a framework using harmonic torsional diffusion to improve flexible protein-ligand docking by modeling rotational motion on a circle. Harmony is a method for flexible protein-ligand docking that uses learned harmonic potentials on the circle to model torsional scores in a way that respects periodicity. This approach makes the model frequency-aware and improves pose accuracy and physical validity in docking simulations. The paper demonstrates that aligning score parameterization with diffusion geometry is an effective lever for enhancing flexible docking performance. Harmony is a method for flexible protein-ligand docking that uses harmonic potentials on the circle to explicitly incorporate periodic geometry into torsional diffusion. This work shows how modeling rotational motion via harmonic potentials on a circle improves the accuracy of ligand pose prediction in flexible docking. The paper proves that aligning score parameterization with the geometry of the diffusion process is a simple and effective way to improve flexible docking. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle. This framework makes periodicity explicit and gives the model a frequency-aware inductive bias over rotameric motion. The results show Harmony improves ligand pose accuracy and pocket reconstruction on PDBBind and PoseBusters benchmarks. Case studies confirm its effectiveness on different binding site geometries. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model the complex conformational changes in protein-ligand binding by parameterizing torsional scores using harmonic potentials on the circle. This framework makes periodicity explicit and provides a frequency-aware inductive bias over rotameric motion, leading to improved docking accuracy. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which respects the geometry of the torus. The results show improvements in pose accuracy and physical validity across various benchmarks. This paper introduces Harmony, a framework using harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on a circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model the complex conformational changes in protein-ligand binding by explicitly incorporating periodic geometry into the score field. This approach leads to improved ligand pose prediction and pocket reconstruction compared to existing methods. The paper demonstrates that aligning score parameterization with diffusion geometry is an effective lever for improving flexible docking accuracy. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit. This leads to a frequency-aware inductive bias over rotameric motion and better performance on benchmarks like PDBBind and PoseBusters. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better results in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves pose accuracy. This paper introduces Harmony, a framework using harmonic torsional diffusion to explicitly handle periodic geometry in flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on a circle. The results show that aligning score parameterization with diffusion geometry is an effective way to improve flexible docking performance across different benchmarks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better results in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This work shows that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The paper introduces Harmony, a framework using harmonic torsional diffusion to better model flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better performance in flexible docking tasks. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which improves ligand pose accuracy and pocket reconstruction. This paper demonstrates that aligning score parameterization with diffusion geometry is a simple lever for improving flexible docking performance. The core idea of Harmony is to use harmonic torsional diffusion to better handle flexible protein-ligand docking by parameterizing torsional scores with learned harmonic potentials on the circle. Harmony is a method for flexible protein-ligand docking that uses harmonic torsional diffusion to model ligand and side-chain torsion as derivatives of learned harmonic potentials on the circle, which makes periodicity explicit and improves physical validity in complex binding scenarios. This framework provides a frequency-aware inductive bias over rotameric motion, leading to better [paper] [episode]

The papers

• Harmonic Torsional Diffusion for Protein-Ligand Flexible Docking — The gist The introduction proposes Harmony, a harmonic torsional diffusion framework for flexible protein-ligand docking, which parameterizes ligand and side-chain torsional score fields as derivatives of learned harmonic potentials on the circle to explicitly make periodicity ex [episode]

Important terms

protein-ligand docking

This is the process of predicting how a small molecule binds to a protein, which this work aims to make more accurate when both molecules can move flexibly during binding.

diffusion models

These are machine learning methods used here that are being improved. The current versions struggle because they don't properly handle the repeating, periodic nature of how parts of a molecule twist and turn.

Harmony

This is the new framework introduced. It uses learned harmonic potentials on a circle to describe the twisting motions of ligands and side chains in a way that respects their periodic nature.

torsional score fields

These are mathematical functions that help predict how good a certain rotational position (torsion) is for the ligand, and Harmony learns these fields specifically for this task.

Fourier basis

This is a mathematical tool used to break down complex signals. The research uses it to introduce noise in a way that makes the periodicity of the torsional motions clear to the model.