Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models

Jack Simons, Louis Sharrock, Song Liu, Mark Beaumont

Keywords: Likelihood-free inference, simulation-based inference, score based diffusion models, amortized inference, score matching

TL;DR: We adapt condition score based diffusion models for usage in simulation-based inference contexts.

Abstract:

In recent years, score based diffusion models have achieved remarkable empirical performance across a wide range of generative modelling tasks. In this paper, we study the use of conditional score-based diffusion models for Bayesian inference in simulator-based models.
We consider two objectives for training these models, one of which approximates the score of the diffused likelihood, while the other directly estimates the score of the diffused posterior.
We validate these methods, which we term Neural Posterior Score Estimation (NPSE) and Neural Likelihood Score Estimation (NLSE), on several numerical examples, demonstrating comparable or superior performance to existing state-of-the-art methods such as Neural Posterior Estimation (NPE) and Neural Likelihood Estimation (NLE).