Backward SDEs-based Diffusion for Physics-Constrained Generation
cs.LG
Submitted: 2026-09-14
Updated: 2026-09-14
Comments: Accepted as ICML paper
Journal ref: Zihao Wang, Backward SDEs-based Diffusion for Physics-Constrained Generation, Forty-third International Conference on Machine Learning 2026
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
The gist: Pretrained score-based diffusion models provide strong unconditional priors, yet enforcing measurement or physics consistency in inverse problems is often handled by heuristic guidance, intermittent
Terminology
Abstract
Pretrained score-based diffusion models provide strong unconditional priors, yet enforcing measurement or physics consistency in inverse problems is often handled by heuristic guidance, intermittent projections, or task-specific conditional training, with limited guarantees of feasibility at the end of inference. We propose terminal-conditioned inversion for score-based SDE priors. Given a frozen Score-SDE prior and a task-defined terminal feasibility specification, we construct an associated backward stochastic differential equation whose adapted solution defines a principled inverse map from the terminal requirement to a prior state at a chosen noise level. Under standard regularity conditions, we establish existence and uniqueness of the adapted solution and obtain terminal consistency by construction. We further develop a practical neural BSDE solver that composes arbitrary pretrained diffusion priors with domain constraints without modifying the score-defined coefficients, producing an anchored prior state that enables neighborhood sampling for uncertainty characterization. Experiments on toy datasets validate stable terminal-conditioned inversion and distributionally consistent neighborhood sampling. As a real-world case study, we apply the framework to sparse-view CT reconstruction and achieve improved reconstruction quality over representative training-free baselines while satisfying strict measurement feasibility under the prescribed terminal specification. Project is available in: https://laplace.center/icmlbsdeI/
Sources
- Flow Matching on General Geometries
- Deep Diffusion Image Prior for Efficient OOD Adaptation in 3D Inverse Problems
- Improving Diffusion Models for Inverse Problems using Manifold Constraints
- Simulating Diffusion Bridges with Score Matching
- Denoising Diffusion Restoration Models
- Image Restoration using Total Variation Regularized Deep Image Prior
- Score-Based Generative Modeling through Stochastic Differential Equations
- Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model
- Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guarantees
- Denoising Diffusion Models for Plug-and-Play Image Restoration
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