Research map / Image generation / Fast diffusion sampling
The Poisson Midpoint Method for Langevin Dynamics: Provably Efficient Discretization for Diffusion Models
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes the Poisson Midpoint Method, a randomized midpoint variant of Langevin Monte Carlo that approximates K small Euler-Maruyama steps with one large step, proves a quadratic speedup under LSI, and applies it as a training-free DDPM scheduler for latent diffusion models.
Problem
Langevin Monte Carlo and DDPM samplers need many small steps for good quality; existing randomized midpoint analyses only cover strongly log-concave targets, while diffusion models involve non-log-concave, time-varying drifts.
Approach
Replace K small Euler-Maruyama steps with one step of size alpha by sampling a discrete set of midpoints (Bernoulli or uniform selection) where the drift is evaluated at a cheap interpolated point, and correct the update; analyze the resulting noise via a Wasserstein CLT so the KL error holds without isoperimetry or strong log-concavity.
Key results
- Poisson Midpoint Method matches DDPM with 1000 neural network calls using roughly 40-80 neural network calls across datasets, per the paper's Table of results.
- Outperforms DDIM and DPM-Solver in FID/CLIP-FID at comparable neural network call budgets (50-80 calls), while DPM-Solver remains best at about 10 steps.
- Theoretically, PLMC achieves a quadratic speedup over LMC in TV distance under LSI, improving ULMC complexity from 1/eps^{2/3} to 1/sqrt(eps) in the stated comparison.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Poisson Midpoint sampling instead of the DDPM scheduler | Latent Diffusion Model · Image-generation datasets in the experiments | sample quality: 1000 neural network calls -> 40-80 neural network calls | Helped |
| Use Poisson Midpoint sampling instead of ODE-based samplers | Latent Diffusion Model · Image-generation datasets, similar compute | sample quality: 50-80 neural network calls | Helped |
| Use DPM-Solver rather than Poisson Midpoint sampling | Latent Diffusion Model · Very low compute regime (~10 steps) | sample quality: ~10 steps | Hurt |
| Reduce Gaussian variance in Poisson Midpoint Variant 1 (ablation) | Poisson Midpoint Method · Diffusion models with a small number of diffusion steps | FID or Clip-FID | Helped |
| Increase Gaussian variance in Poisson Midpoint Variant 1 (ablation) | Poisson Midpoint Method · Diffusion models with a larger number of diffusion steps | FID or Clip-FID | Helped |
| Use Option 2 without-replacement midpoint sampling instead of Option 1 (ablation) | Poisson Midpoint Method · Diffusion models with a lower number of steps | convergence | Helped |
| Use Poisson Midpoint sampling with around 40-50 neural network calls | Latent Diffusion Model · Image-generation datasets | sample quality: 40-50 neural network calls | Hurt |
| Vary DDPM coefficients across its three variants (ablation) | DDPM scheduler · CelebAHQ 256, LSUN Churches, LSUN Bedrooms, and FFHQ 256 | FID or Clip-FID: steps less than or equal to 125 | Mixed |
Surprising findings
- Quality degrades rapidly below about 40-50 neural network calls, attributed to breakdown of the stochastic approximation at large step sizes.
- The best DDPM variant and best Poisson Midpoint variant change with step count, with different coefficient choices winning in different regimes.
Limitations
- Quality degrades rapidly at around 40-50 neural network calls.
- Theory relies on constants and lower-order terms; guarantees are on KL/TV with strong assumptions for the ULMC/OLMC bounds (smoothness, moment bounds).
- Requires variance-correction heuristics for large K.
Experimental setup
Datasets: CelebAHQ 256 LSUN Churches LSUN Bedrooms FFHQ 256
Benchmarks: CelebAHQ 256 LSUN Churches LSUN Bedrooms FFHQ 256
Metrics: FID CLIP-FID
Baselines: DDPM DDIM DPM-Solver PNDM
Builds on: Randomized Midpoint Method DDPM DDIM DPM-Solver
Closest papers by meaning
- Langevin Monte Carlo for strongly log-concave distributions: Randomized midpoint revisited (ICLR 2024 · similarity 0.92)
- Sequential Controlled Langevin Diffusions (ICLR 2025 · similarity 0.89)
- Posterior Sampling by Combining Diffusion Models with Annealed Langevin Dynamics (NeurIPS 2025 · similarity 0.88)
- Wasserstein Convergence of Critically Damped Langevin Diffusions (NeurIPS 2025 · similarity 0.88)
- Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics (ICLR 2025 · similarity 0.88)
- Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallel (ICLR 2025 · similarity 0.88)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.