No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplers

2025-02-10

AI Summary

This work addresses the problem of training neural samplers without access to simulated trajectories, for efficient sampling from high-dimensional distributions specified only by their unnormalized densities (i.e., known up to a normalizing constant). Existing simulation-free methods often suffer from mode collapse due to the lack of dynamical priors. To address this, we first systematically identify Langevin preconditioning as critical for stabilizing training and preserving multimodal structure. We then propose a novel baseline integrating Parallel Tempering (PT) with generative models, and provide theoretical analysis grounded in time-dependent normalizing flows and variational objectives. Empirical results demonstrate that simulation-free training without Langevin preconditioning consistently fails in practice. In contrast, PT-enhanced generative modeling achieves substantial improvements in sample quality and full-mode coverage on benchmark tasks, establishing it as a strong, robust baseline for simulation-free sampling.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Natural Language Processing: Generation
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Search and Retrieval-Augmented AI: Large language models for search
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

We consider the sampling problem, where the aim is to draw samples from a distribution whose density is known only up to a normalization constant. Recent breakthroughs in generative modeling to approximate a high-dimensional data distribution have sparked significant interest in developing neural network-based methods for this challenging problem. However, neural samplers typically incur heavy computational overhead due to simulating trajectories during training. This motivates the pursuit of simulation-free training procedures of neural samplers. In this work, we propose an elegant modification to previous methods, which allows simulation-free training with the help of a time-dependent normalizing flow. However, it ultimately suffers from severe mode collapse. On closer inspection, we find that nearly all successful neural samplers rely on Langevin preconditioning to avoid mode collapsing. We systematically analyze several popular methods with various objective functions and demonstrate that, in the absence of Langevin preconditioning, most of them fail to adequately cover even a simple target. Finally, we draw attention to a strong baseline by combining the state-of-the-art MCMC method, Parallel Tempering (PT), with an additional generative model to shed light on future explorations of neural samplers.

Problem

• Simulation-free training of neural samplers
• Avoiding mode collapse in neural samplers
• Enhancing coverage of target distributions

Innovation

• Simulation-free training via normalizing flow
• Langevin preconditioning prevents mode collapse
• Combining MCMC with generative models