Schr"odinger Bridges on Lie Group Manifolds for Probabilistic Intrinsic Generation

arXiv:2609.02196 · stat.ML, cs.AI, cs.LG · Submitted 2026-09-02 · Read on arXiv

stat.ML, cs.AI, cs.LG

Submitted: 2026-09-02

Updated: 2026-09-02

Code: https://github.com/cafferyzhang12/Schr-dinger_

Terminology

• Calibration — 38× in this paper · explained in 7 episodes
• Benchmark — 35× in this paper · explained in 2 episodes
• Consistency — 17× in this paper · explained in 3 episodes
• Generative Modeling — 16× in this paper · explained in 3 episodes
• Ablation — 14× in this paper · explained in 1 episode
• Verification — 8× in this paper · explained in 2 episodes
• Accuracy — 6× in this paper · explained in 1 episode
• Flow Matching — 6× in this paper · explained in 8 episodes
• Diffusion Model — 4× in this paper · explained in 8 episodes
• Diffusion Models — 4× in this paper · explained in 6 episodes
• Normalizing Flow — 4× in this paper · explained in 3 episodes
• Normalizing Flows — 4× in this paper · explained in 4 episodes
• Alignment — 3× in this paper · explained in 1 episode
• Fidelity — 3× in this paper · explained in 2 episodes
• Negative Log-Likelihood — 3× in this paper
• Optimal Transport — 3× in this paper · explained in 5 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Ablation Studies — 2× in this paper · explained in 1 episode
• Aggregation — 2× in this paper · explained in 1 episode
• Core — 2× in this paper · explained in 2 episodes
• Data Augmentation — 2× in this paper · explained in 7 episodes
• Effective Sample Size — 2× in this paper
• Embeddings — 2× in this paper · explained in 2 episodes
• Error Decomposition — 2× in this paper · explained in 3 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Reciprocal Conditional-Control Bridge Matching — 2× in this paper
• Riemannian Flow Matching — 2× in this paper
• Steering — 2× in this paper · explained in 2 episodes
• Stochastic Dynamics — 2× in this paper · explained in 2 episodes
• Wrapped-Kernel Bridge Calibration — 2× in this paper
• Antithetic sampling — 1× in this paper · explained in 1 episode
• Computational overhead — 1× in this paper · explained in 2 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Diffusion Processes — 1× in this paper · explained in 2 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Models — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Magnus Expansion — 1× in this paper · explained in 4 episodes
• Maximum Mean Discrepancy — 1× in this paper
• Ornstein–Uhlenbeck Process — 1× in this paper · explained in 3 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Representation Learning — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Transverse Field Ising Model — 1× in this paper
• Trivialized Momentum Diffusion Models — 1× in this paper
• WKBC with Riemannian Diffusion Models — 1× in this paper

Sources

• Diffusion Generative Modeling on Lie Group Representations
• Riemannian Diffusion Schr\"odinger Bridge

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