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Posterior Sampling by Combining Diffusion Models with Annealed Langevin Dynamics

NeurIPS 2025 · Image generation › Fast diffusion sampling · approach: Diffusion theory and learned samplers · 0 citations (OpenAlex)

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Shows that combining a diffusion model prior (for a warm start) with annealed Langevin dynamics gives polynomial-time posterior sampling for log-concave (globally or locally) priors using only an L^4 score-error bound, with a compressed-sensing corollary and FFHQ-256 inpainting/SR/deblurring experiments.

Problem

Posterior sampling p(x|y) from a noisy linear measurement y=Ax+noise given an approximate prior score; existing diffusion-based heuristics lack guarantees and Langevin needs MGF-accurate scores.

Approach

Use a noise-annealed sequence of intermediate posteriors p(x|y_i), with short Langevin mixing steps between consecutive levels, starting from a diffusion-model sample; for log-concave (or locally log-concave) priors this keeps the process near the prior manifold so only an L^4 score-error bound is needed.

Key results

• In inpainting, with sufficiently small step size, the annealed Langevin refinement surpasses DPS on both L2 distance and FID on 1k FFHQ-256 validation images.
• Across all three tasks, more annealed Langevin time decreases L2 error but increases FID.
• Theory: polynomial-time posterior sampling for alpha-strongly log-concave priors with only an L^4 score-error bound (epsilon_score <= sqrt(alpha)/K_1).

Measured effects reported in the paper

Surprising findings

• Experiments show a trade-off: longer annealed Langevin improves L2 but worsens FID, so the method is not uniformly better than DPS.

Limitations

• Theoretical guarantees require (local) log-concavity of the prior, which real image manifolds may not satisfy.
• Experiments are on three linear inverse problems on FFHQ-256 and use DPS for initialization, so gains depend on the heuristic warm start.

Experimental setup

Datasets: FFHQ-256

Benchmarks: FFHQ-256 inpainting FFHQ-256 4x super-resolution FFHQ-256 Gaussian deblurring

Metrics: L2 distance to ground truth FID

Baselines: DPS

Builds on: DPS Langevin dynamics diffusion SDE

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