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MaRS: A Fast Sampler for Mean Reverting Diffusion based on ODE and SDE Solvers
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Proposes MR Sampler, a training-free fast solver for Mean Reverting (MR) Diffusion that solves its reverse SDE and PF-ODE semi-analytically, giving 10-20x speedups over posterior sampling across ten image restoration tasks.
Problem
MR Diffusion (mean-reverting SDE) for image-conditioned generation requires hundreds of NFEs, and existing training-free fast samplers (designed for VPSDE/VESDE with linear drift) cannot be applied to its affine drift.
Approach
Derive a semi-analytical solution of the MRSDE reverse SDE and PF-ODE, where the analytic part is computed exactly and only the integral of the network output is approximated with exponential integrators (multistep backward differences), supporting noise, data, and velocity parameterizations; data prediction is shown to be numerically more stable.
Key results
- MR Sampler maintains high sampling quality with a 10 to 20 times speedup across ten image restoration tasks.
- Sampler converges in 5 or 10 NFEs with high sampling quality.
- Data prediction is numerically more stable than noise prediction at small NFEs, where noise-prediction sampling can perform worse than posterior sampling.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MR Sampler instead of the existing MR Diffusion sampling method | MR Diffusion · Ten image restoration tasks | sampling speedup: 10 to 20 times | Helped |
| Use data prediction rather than noise prediction (ablation) | MR Sampler · Image restoration with small NFEs | sampling quality | Helped |
| Use noise prediction rather than data prediction (ablation) | MR Sampler · Image restoration with small NFEs | sampling quality | Hurt |
Surprising findings
- Noise-prediction parameterization becomes markedly worse than posterior sampling when NFE is below 20.
Limitations
- Noise-prediction variant unstable at small NFEs
- Convergence radius analysis only approximated via n=1 ratio, not computed exactly
Experimental setup
Benchmarks: ten image restoration tasks
Metrics: sampling quality speedup
Baselines: posterior sampling Heun discretization
Builds on: MR Diffusion (MRSDE) DPM-Solver posterior sampling Karras EDM
Closest papers by meaning
- Fast ODE-based Sampling for Diffusion Models in Around 5 Steps (CVPR 2024 · similarity 0.89)
- Improving Diffusion Posterior Samplers with Lagged Temporal Corrections for Image Restoration (NeurIPS 2026 · similarity 0.89)
- CCS: Controllable and Constrained Sampling with Diffusion Models via Initial Noise Perturbation (NeurIPS 2025 · similarity 0.89)
- Enhanced Diffusion Sampling via Extrapolation with Multiple ODE Solutions (ICLR 2025 · similarity 0.88)
- Boosting Diffusion Models with Moving Average Sampling in Frequency Domain (CVPR 2024 · similarity 0.88)
- Fast samplers for Inverse Problems in Iterative Refinement models (NeurIPS 2024 · similarity 0.88)
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