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Stability and Generalizability in SDE Diffusion Models with Measure-Preserving Dynamics
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Proposes D^3GM, a measure-preserving random-dynamical-systems framework for SDE-based transitionary diffusion models that improves stability and generalization for inverse problems (deraining, dehazing, MRI reconstruction and super-resolution).
Problem
Transitionary SDE diffusion models for inverse problems are unstable and generalize poorly under non-uniform noise and corrupted or unknown degradations, with errors accumulating in the reverse process.
Approach
Model the forward degradation as an Ornstein-Uhlenbeck-type SDE with the constraint sigma_t^2/(2 theta_t)=lambda^2 so that the process has a measure-preserving stationary attractor N(mu, lambda^2) (mu = degraded measurement), with an extra scale tau to bring the terminal state closer to the stationary distribution; the reverse process is trained with a score-matching loss.
Key results
- On Rain100H, D3GM reaches 32.41 PSNR / 0.912 SSIM versus 31.65 / 0.904 for IR-SDE (OU).
- On fastMRI at 8x undersampling, D3GM reports 27.92 PSNR and LPIPS 0.175, the best PSNR and LPIPS in that column; at 16x it is 25.26 PSNR, below CDiffMR (25.77).
- On O-HAZE dehazing, D3GM reaches 26.23 PSNR versus 25.31 for the next best (MB-TF); on Dense-Haze it reaches 15.85 PSNR, below Dehamer (16.62).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use D³GM instead of IR-SDE (OU) | D³GM · Rain100H | PSNR: 31.65 -> 32.41 | Helped |
| Use D³GM instead of IR-SDE (OU) | D³GM · Rain100L | PSNR: 38.30 -> 38.40 | Helped |
| Use D³GM instead of MB-TF | D³GM · O-HAZE | PSNR: 25.31 -> 26.23 | Helped |
| Use D³GM instead of Dehamer | D³GM · Dense-Haze | PSNR: 16.62 -> 15.85 | Hurt |
| Use D³GM instead of DiffuseRecon | D³GM · fastMRI, undersampling factor 8x | PSNR: 27.40 -> 27.92 | Helped |
| Use D³GM instead of CDiffMR | D³GM · fastMRI, undersampling factor 16x | PSNR: 25.77 -> 25.26 | Hurt |
| Use D³GM instead of CST | D³GM · IXI T2w X4, Guys | PSNR: 23.70 -> 25.13 | Helped |
| Use D³GM instead of CST | D³GM · IXI T2w X4, IOP | PSNR: 28.55 -> 28.60 | Helped |
| Use D³GM instead of IR-SDE | D³GM · Real Dehazing | PSNR: 24.52 -> 26.23 | Helped |
| Use D³GM instead of DRSformer | D³GM · rain200H | SSIM: 0.933 -> 0.925 | Hurt |
| Use the measure-preserving stationary-process constraint instead of coefficient-decoupled SDE | D³GM · Inverse problems | stability | Helped |
| Set the variance-to-drift ratio to a constant stationary variance | D³GM · Inverse problems | stability | Helped |
Surprising findings
- On Dense-Haze and fastMRI 16x, D3GM does not beat the best baseline in PSNR, with the authors attributing the Dense-Haze gap to severe signal corruption.
Limitations
- Overall restored-image quality is still limited under severe corruption such as real dehazing, consistent with the authors' Prop. 2.
- Theoretical analysis relies on assumptions (Lipschitz, bounded score) and the constraint sigma^2/(2 theta)=lambda^2 that is restrictive in practice.
Experimental setup
Datasets: Rain100H Rain100L O-HAZE Dense-Haze fastMRI IXI
Benchmarks: Rain100H Rain100L O-HAZE Dense-Haze fastMRI x8/x16 IXI MRI SR x4 (HH, Guys, IOP) rain200H
Metrics: PSNR SSIM LPIPS FID Params FLOPs
Baselines: IR-SDE VPB (CD) I2SB DPS CDDB DRSformer DiffuseRecon CDiffMR SwinMR Restormer Dehamer MB-TF
Builds on: IR-SDE score-based SDE Schrodinger bridge (I2SB) SDEdit
Closest papers by meaning
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.90)
- SITCOM: Step-wise Triple-Consistent Diffusion Sampling For Inverse Problems (ICML 2025 · similarity 0.89)
- Coupled Data and Measurement Space Dynamics for Enhanced Diffusion Posterior Sampling (NeurIPS 2025 · similarity 0.88)
- System-Embedded Diffusion Bridge Models (NeurIPS 2025 · similarity 0.88)
- DiffusionPDE: Generative PDE-Solving under Partial Observation (NeurIPS 2024 · similarity 0.88)
- Diffusion Bridge Implicit Models (ICLR 2025 · similarity 0.88)
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