Neural posterior estimation (NPE), a simulation-based computational approach for Bayesian inference, has shown great success in situations where posteriors are intractable or likelihood functions are treated as "black boxes." Existing NPE methods typically rely on normalizing flows, which transform a base distributions into a complex posterior 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 as an alternative to normalizing flows for 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. These gains persist across a variety of different encoder or "summary network" architectures, as well as in situations where no summary network is required. The code will be publicly available at \url{https://github.com/TianyuCodings/cDiff}.

翻译：神经后验估计（NPE）作为一种基于模拟的贝叶斯推断计算方法，在后验分布难以处理或似然函数被视为“黑箱”的场景中已展现出巨大成功。现有的NPE方法通常依赖于归一化流，其通过组合多个简单可逆变换将基础分布转化为复杂后验。然而，尽管基于流的模型在NPE领域处于前沿水平，但已知存在若干局限性，包括训练不稳定性以及表征能力与计算成本间的尖锐权衡。本研究表明，条件扩散模型可作为NPE中归一化流的有效替代方案。条件扩散模型解决了基于流的方法面临的诸多挑战。实验结果表明：在针对NPE架构的多样化基准测试问题集中，扩散模型即使采用更简单、更浅层的结构，仍能提供更稳定的训练过程、更优越的精度以及更快的训练速度。这些优势在不同编码器或“摘要网络”架构中均得以保持，且在无需摘要网络的情况下同样成立。代码将公开于 \url{https://github.com/TianyuCodings/cDiff}。