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Diffusion Path Samplers via Sequential Monte Carlo

NeurIPS 2026 · Image generation › Fast diffusion sampling · approach: Diffusion theory and learned samplers · 0 citations (OpenAlex)

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Proposes diffusion path SMC (DPSMC), a training-free sampler that estimates diffusion-path scores with sequential Monte Carlo over auxiliary posterior variables, plus optimal control-variate score identities and a cosine schedule.

Problem

Sampling from unnormalised target densities via diffusion paths requires accurate score estimates of time-varying path marginals, which existing MCMC- or rejection-based estimators make costly and sequential.

Approach

Estimate path-marginal scores and densities by SMC over auxiliary variables evolving along posterior distributions, combined with variance-minimising matrix control-variate score identities and a KL-action-motivated cosine diffusion schedule, yielding batchable, unbiased density estimates.

Key results

• On GMM40 (d=50), DPSMC (LL/DALD variants) reduces entropy-regularised W2 to about 27-29 versus 79-115 for AIS, SMC and RDMC, with DPSMC using about 1K batched energy evaluations vs 131K for AIS/SMC.
• On Funnel (d=10), DPSMC (OU) gets KS 0.028 versus 0.073 for SLIPS and 0.082 for RDMC, and log Z bias 0.12 versus 0.28 for AIS/SMC in the normalising-constant table.
• On Bayesian logistic regression, DPSMC (OU) achieves the best test log-likelihood on Ionosphere (-83.73) and Sonar (-108.23).

Surprising findings

• Starting sampling from a non-Gaussian point with a later time (LL initialisation) or accepting poorly sampled posterior particles early on does not significantly degrade score error.

Limitations

• Importance weights can have considerable variance when embedded in nested RDSMC.
• Dirac contraction of the posterior causes instability late in the path.
• Score estimates are biased due to self-normalisation.

Experimental setup

Datasets: Ionosphere Sonar

Benchmarks: GMM40 Rings Funnel Ionosphere Sonar

Metrics: entropy-regularised W2 sliced KS distance predictive log-likelihood total variation distance log normalising constant bias batched energy evaluations

Baselines: AIS SMC RDMC SLIPS RDSMC

Builds on: rdsmc denoising score identity target score identity diffusion-annealed langevin dynamics stochastic interpolants

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