Sequential Controlled Langevin Diffusions
Junhua Chen, Lorenz Richter, Julius Berner, Denis Blessing, Gerhard Neumann, Anima Anandkumar
TL;DR
This paper introduces Sequential Controlled Langevin Diffusion (SCLD), a novel sampling method combining Sequential Monte Carlo and diffusion-based techniques, leading to improved efficiency and performance in sampling from complex distributions.
Contribution
The paper develops a unified continuous-time framework for combining SMC and diffusion-based samplers, resulting in the SCLD method with enhanced sampling efficiency.
Findings
SCLD outperforms existing methods on benchmark problems.
SCLD requires only 10% of the training budget of previous diffusion samplers.
Combining SMC and diffusion approaches leverages their complementary strengths.
Abstract
An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where the transport is performed through successive annealed densities via prescribed Markov chains and resampling steps, and (2) recently developed diffusion-based sampling methods, where a learned dynamical transport is used. Despite the common goal, both approaches have different, often complementary, advantages and drawbacks. The resampling steps in SMC allow focusing on promising regions of the space, often leading to robust performance. While the algorithm enjoys asymptotic guarantees, the lack of flexible, learnable transitions can lead to slow convergence. On the other hand, diffusion-based samplers are learned and can potentially better adapt…
Peer Reviews
Decision·ICLR 2025 Poster
The paper is well-written and I find the results to be of significant interest to the Bayesian statistics community -- SMC has become an important statistical tools for simulating samples from intractable densities, and I think merging SMC with diffusion gives useful insights in building more flexible SMC samplers. While some of the paper's contributions seem incremental, the resulting algorithm seems more useful in practice when compared to its predecessor work CMCD, mainly thanks to its use
I have a positive assessment of this paper, and I enjoyed reading it overall. The overall contribution of this paper seems somewhat limited. It is somewhat difficult to pinpoint exactly what is new from this paper, although I think the overall readability and SCLD's potential usefulness make up for this weakness. I think the main weakness of this paper is that the combination of continuous and discrete time seems somewhat arbitrary. It seems to me that given enough training iterations, SCLD o
This paper is presented clearly and in detail, making it easy for readers to follow. The proposed framework also allows the authors to design suitable loss functions compatible with off-policy training, which has greatly reduced the use of the training budget in practice. Extensive numerical experiments are provided to validate the effectiveness of the SCLD method.
1. As the SCLD algorithm relies on the diffusion bridge formulation, the reviewer thinks that it might be necessary to include a short literature review on related work [1,2,3] combining diffusion bridges/stochastic optimal control with generative models for the sake of completeness. However, this is missing in the current version of the manuscript. 2. Though the framework based on path measures proposed in this paper leads to effective sampling methods, the idea of combining SMC with diffusio
- The integration of SMC and diffusion-based sampling represents a novel and promising approach to tackling challenges in high-dimensional sampling. - The paper is generally well-structured, with clear segmentation between theory, algorithmic details, and experimental evaluation. - The proposed log-variance divergence loss function could have meaningful applications in high-dimensional probabilistic modeling, particularly for tasks prone to mode collapse and instability.
While the proposed method is conceptually reasonable, the writing is quite sloppy. It is hard for me to understand the contribution and advantages of the proposed SCLD. - The authors claim that the KL divergence estimator suffers from exponential error growth (Proposition 2.4) and the authors instead use log-variance divergence (Equation (18)). However, there is no formal proof or quantitative scaling analysis of this claim using the log-variance divergence. - The use of "off-policy training" s
Videos
Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Gene Regulatory Network Analysis · Bayesian Methods and Mixture Models
MethodsDiffusion