Latent Target Score Matching, with an application to Simulation-Based Inference

TL;DR

This paper introduces Latent Target Score Matching (LTSM), a novel method that improves score estimation in diffusion models with latent variables, enhancing variance reduction and sample quality in simulation-based inference.

Contribution

LTSM extends Target Score Matching to handle latent variables by leveraging joint scores, improving score accuracy and robustness across noise levels.

Findings

LTSM reduces variance in score estimation.

LTSM improves sample quality in experiments.

Combining LTSM with DSM enhances robustness.

Abstract

Denoising score matching (DSM) for training diffusion models may suffer from high variance at low noise levels. Target Score Matching (TSM) mitigates this when clean data scores are available, providing a low-variance objective. In many applications clean scores are inaccessible due to the presence of latent variables, leaving only joint signals exposed. We propose Latent Target Score Matching (LTSM), an extension of TSM to leverage joint scores for low-variance supervision of the marginal score. While LTSM is effective at low noise levels, a mixture with DSM ensures robustness across noise scales. Across simulation-based inference tasks, LTSM consistently improves variance, score accuracy, and sample quality.