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Sequential Controlled Langevin Diffusions
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Combines Sequential Monte Carlo with learned controlled Langevin diffusions in continuous time via path-space importance weights, training with a log-variance loss and replay buffers to yield the SCLD sampler.
Problem
Sampling from unnormalized densities: SMC relies on fixed MCMC transitions that converge slowly, while diffusion-based samplers are learned but suffer from training instability and mode collapse.
Approach
Views SMC and diffusion samplers in continuous time as path-space measures, deriving Radon-Nikodym weights for controlled Langevin SDEs over subtrajectories so resampling and MCMC can be interleaved with a learned control, trained end-to-end with a log-variance divergence and prioritized replay buffers.
Key results
- SCLD achieves the best ELBO on Seeds (-73.45), Sonar (-108.17), Credit (-504.46) and Brownian (1.00) among compared methods.
- On Robot1 and Robot4 SCLD gets Sinkhorn distances of 0.31 and 0.40, far below the next best baseline (1.54 for PIS on Robot1 and SMC-FC 0.37 on Robot1 is not best overall), while GMM40 Sinkhorn drops to 3787.73 vs 4258.57 for CMCD-LV.
- SCLD surpasses CMCD-KL and CMCD-LV trained for 40000 gradient steps using only 3000 steps, reportedly around 10% of the training budget.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SCLD instead of CMCD-KL | sampling method · Seeds (26d) | ELBO: -73.51 -> -73.45 | Helped |
| Use SCLD instead of SMC-FC | sampling method · Sonar (61d) | ELBO: -108.93 -> -108.17 | Helped |
| Use SCLD instead of CMCD-LV | sampling method · Credit (25d) | ELBO: -504.90 -> -504.46 | Helped |
| Use SCLD instead of CRAFT | sampling method · Brownian (32d) | ELBO: 0.90 -> 1.00 | Helped |
| Use SCLD instead of SMC-ESS | sampling method · LGCP (1600d) | ELBO: 497.85 -> 486.77 | Hurt |
| Use SCLD instead of CMCD-KL | sampling method · Funnel (10d) | Sinkhorn distance: 124.89 -> 134.23 | Hurt |
| Use SCLD instead of PIS | sampling method · MW54 (5d) | Sinkhorn distance: 0.42 -> 0.44 | Hurt |
| Use SCLD instead of SMC-FC | sampling method · Robot1 (10d) | Sinkhorn distance: 0.37 -> 0.31 | Helped |
| Use SCLD instead of SMC-FC | sampling method · Robot4 (10d) | Sinkhorn distance: 1.23 -> 0.40 | Helped |
| Use SCLD instead of CMCD-LV | sampling method · GMM40 (50d) | Sinkhorn distance: 4258.57 -> 3787.73 | Helped |
| Use SCLD instead of SMC-ESS | sampling method · MoS (50d) | Sinkhorn distance: 1477.04 -> 656.10 | Helped |
| Add SMC steps during training and evaluation rather than using zero SMC steps (CMCD) (ablation) | SCLD · multiple sampling benchmarks | benchmark performance | Helped |
Surprising findings
- CRAFT and CMCD-KL collapse to a single mode on Robot4, while CMCD-LV finds no accurate mode and only SCLD samples all 8 modes.
- Zero SMC steps recovers CMCD, and adding SMC steps only at evaluation already improves over standalone diffusion samplers.
Limitations
- Multinomial resampling and mode collapse risk on highly multimodal targets when resampling is used heavily
- KL divergence estimator variance scales exponentially with dimension, so the method relies on the log-variance loss
- Prescribed annealing path requires the target density; learned marginals are not explored in main method
Experimental setup
Datasets: Seeds Sonar Credit Brownian LGCP Funnel MW54 GMM40 MoS Robot1 Robot4
Benchmarks: Seeds Sonar Credit Brownian LGCP Funnel MW54 GMM40 MoS Robot1 Robot4
Metrics: ELBO Sinkhorn distance
Baselines: SMC SMC-ESS SMC-FC CRAFT DDS PIS CMCD-KL CMCD-LV
Builds on: CMCD CRAFT PDDS Denoising Diffusion Samplers log-variance loss
Closest papers by meaning
- Reverse Diffusion Sequential Monte Carlo Samplers (NeurIPS 2025 · similarity 0.91)
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- Tuning Sequential Monte Carlo Samplers via Greedy Incremental Divergence Minimization (ICML 2025 · similarity 0.90)
- The Poisson Midpoint Method for Langevin Dynamics: Provably Efficient Discretization for Diffusion Models (NeurIPS 2024 · similarity 0.89)
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