Conditional diffusions for amortized neural posterior estimation

TL;DR

This paper introduces conditional diffusion models combined with high-capacity summary networks for neural posterior estimation, demonstrating improved stability, accuracy, and training efficiency over traditional flow-based methods.

Contribution

It presents a novel application of conditional diffusions for amortized NPE, overcoming limitations of flow-based models and showing consistent performance improvements.

Findings

Diffusions outperform flow-based models in stability and accuracy.

Training times are faster with diffusion-based NPE.

Results are consistent across various network architectures.

Abstract

Neural posterior estimation (NPE), a simulation-based computational approach for Bayesian inference, has shown great success in approximating complex posterior distributions. Existing NPE methods typically rely on normalizing flows, which approximate a distribution by composing many simple, invertible transformations. But flow-based models, while state of the art for NPE, are known to suffer from several limitations, including training instability and sharp trade-offs between representational power and computational cost. In this work, we demonstrate the effectiveness of conditional diffusions coupled with high-capacity summary networks for amortized NPE. Conditional diffusions address many of the challenges faced by flow-based methods. Our results show that, across a highly varied suite of benchmarking problems for NPE architectures, diffusions offer improved stability, superior accuracy, and faster training times, even with simpler, shallower models. Building on prior work on diffusions for NPE, we show that these gains persist across a variety of different summary network architectures. Code is available at https://github.com/TianyuCodings/cDiff.