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Main Authors: Lam, Kevin H., Farghly, Tyler, Williams, Christopher, Yang, Jun, Teh, Yee Whye, Doucet, Arnaud
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2605.09654
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author Lam, Kevin H.
Farghly, Tyler
Williams, Christopher
Yang, Jun
Teh, Yee Whye
Doucet, Arnaud
author_facet Lam, Kevin H.
Farghly, Tyler
Williams, Christopher
Yang, Jun
Teh, Yee Whye
Doucet, Arnaud
contents Sampling from score-based diffusion models incurs bias due to both time discretisation and the approximation of the score function. A common strategy for reducing this bias is to apply corrector steps based on the unadjusted Langevin algorithm (ULA) at each noise level within a predictor-corrector framework. However, ULA is itself a biased sampler, as it discretises a continuous diffusion process. In this work, we consider adjusted Langevin correctors that employ Metropolis--Hastings (MH) or Barker's accept-reject steps to correct for this bias. Since the target density ratio typically required by MH-based algorithms is unavailable, we propose methods that instead utilise the score function to compute the correct acceptance probability. We introduce the first exact method for adjusting Langevin corrections in diffusion models, based on a two-coin Bernoulli factory algorithm. We also propose an efficient approximation based on Simpson's rule that achieves accuracy of order $5/2$ in the step size at near-zero marginal cost. We demonstrate that these procedures improve sample quality on both synthetic and image datasets, yielding consistent gains in Fréchet Inception Distance (FID) on the latter.
format Preprint
id arxiv_https___arxiv_org_abs_2605_09654
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Metropolis-Adjusted Diffusion Models
Lam, Kevin H.
Farghly, Tyler
Williams, Christopher
Yang, Jun
Teh, Yee Whye
Doucet, Arnaud
Machine Learning
Computation
Sampling from score-based diffusion models incurs bias due to both time discretisation and the approximation of the score function. A common strategy for reducing this bias is to apply corrector steps based on the unadjusted Langevin algorithm (ULA) at each noise level within a predictor-corrector framework. However, ULA is itself a biased sampler, as it discretises a continuous diffusion process. In this work, we consider adjusted Langevin correctors that employ Metropolis--Hastings (MH) or Barker's accept-reject steps to correct for this bias. Since the target density ratio typically required by MH-based algorithms is unavailable, we propose methods that instead utilise the score function to compute the correct acceptance probability. We introduce the first exact method for adjusting Langevin corrections in diffusion models, based on a two-coin Bernoulli factory algorithm. We also propose an efficient approximation based on Simpson's rule that achieves accuracy of order $5/2$ in the step size at near-zero marginal cost. We demonstrate that these procedures improve sample quality on both synthetic and image datasets, yielding consistent gains in Fréchet Inception Distance (FID) on the latter.
title Metropolis-Adjusted Diffusion Models
topic Machine Learning
Computation
url https://arxiv.org/abs/2605.09654