Research map / Probabilistic and scientific modeling / Variational and generative sampling
Transport meets Variational Inference: Controlled Monte Carlo Diffusions
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Proposes a path-space variational framework linking optimal transport and VI, derives EM–IPF correspondence, and introduces CMCD, a controlled score-based annealed sampler that learns forward and backward dynamics jointly.
Problem
Sampling from unnormalised densities and estimating normalising constants, and generative modelling, where diffusion models usually fix one of the forward/backward processes and admit non-unique couplings when both are learned.
Approach
Frame generative modelling and sampling as divergence minimisation between forward and reverse path measures; add a score constraint on the backward drift (b_t = a_t - 2σ²∇log π_t) that restores uniqueness, yielding CMCD which learns a control drift for an annealing path of densities and gives zero-variance normalising constant estimates at optimum.
Key results
- Overdamped and underdamped CMCD consistently outperform all baseline methods in mean ELBO over 30 seeds, especially at low Euler steps K.
- On funnel and gmm, CMCD recovers ln Z more consistently than PIS, DDS and SMC, even at low K.
- Across most targets, overdamped CMCD outperforms the underdamped baselines.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CMCD instead of the evaluated baseline methods | Sampling methods · Six standard target distributions | ELBO | Helped |
| Use overdamped CMCD instead of the underdamped baseline methods | Sampling methods · Most of the six standard target distributions | ELBO | Helped |
| Use CMCD instead of PIS, DDS, or SMC | Log-partition estimation · Funnel and GMM | ln Z | Helped |
Surprising findings
- Overdamped CMCD outperforms underdamped baselines on most targets.
Limitations
- Experiments limited to sampling benchmarks with tractable unnormalised densities.
- Empirical exploration of EM vs IPF and regularised IPF left to future work.
Experimental setup
Datasets: funnel gmm
Benchmarks: ELBO on six standard target distributions ln Z estimation on funnel and gmm entropy-regularised OT distance W2 on funnel and gmm
Metrics: ELBO ln Z estimate entropy-regularised Wasserstein-2 distance
Baselines: ULA MCD UHA LDVI PIS DDS SMC
Builds on: Denoising diffusion samplers (DDS) Monte Carlo Diffusion (MCD) Unadjusted Langevin Annealing (ULA) Schrödinger bridge Föllmer drift sampling
Closest papers by meaning
- Variational Schrödinger Diffusion Models (ICML 2024 · similarity 0.90)
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- Diffusion Path Samplers via Sequential Monte Carlo (NeurIPS 2026 · similarity 0.89)
- Sequential Controlled Langevin Diffusions (ICLR 2025 · similarity 0.88)
- Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densities (NeurIPS 2025 · similarity 0.88)
- NETS: A Non-equilibrium Transport Sampler (ICML 2025 · similarity 0.88)
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