# PriorCVAE: scalable MCMC parameter inference with Bayesian deep generative modelling

arXiv: https://arxiv.org/abs/2304.04307 · HTML: https://mlsanity.com/paper/2304.04307/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 63 references that are in the map.
- First posted on arXiv 9 Apr 2023.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Gaussian Processes for Data-Efficient Learning in Robotics and Control](https://mlsanity.com/paper/1502.02860/) (2015)
- [Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC](https://mlsanity.com/paper/1903.08008/) (2019)
- [An Introduction to Probabilistic Programming](https://mlsanity.com/paper/1809.10756/) (2018)
- [Simple and Effective VAE Training with Calibrated Decoders](https://mlsanity.com/paper/2006.13202/) (2020)
- [Neural Diffusion Processes](https://mlsanity.com/paper/2206.03992/) (2022)
- [Diffusion Generative Models in Infinite Dimensions](https://mlsanity.com/paper/2212.00886/) (2022)
- [Bayesian Computing with INLA: A Review](https://mlsanity.com/paper/1604.00860/) (2016)
- [PriorVAE: Encoding spatial priors with VAEs for small-area estimation](https://mlsanity.com/paper/2110.10422/) (2021)
- [An intuitive Bayesian spatial model for disease mapping that accounts for scaling](https://mlsanity.com/paper/1601.01180/) (2016)
- [Spatiotemporal modeling of European paleoclimate using doubly sparse Gaussian processes](https://mlsanity.com/paper/2211.08160/) (2022)

## Built on by (most cited first, 6 of 6)

- [SMRS: advocating a unified reporting standard for surrogate models in the artificial intelligence era](https://mlsanity.com/paper/2502.06753/) (2025)
- [Predictive posterior sampling from non-stationnary Gaussian process priors via Diffusion models with application to climate data](https://mlsanity.com/paper/2505.24556/) (2025)
- [Deep learning and MCMC with aggVAE for shifting administrative boundaries: mapping malaria prevalence in Kenya](https://mlsanity.com/paper/2305.19779/) (2023)
- [Federated Learning for Non-factorizable Models using Deep Generative Prior Approximations](https://mlsanity.com/paper/2405.16055/) (2024)
- [DeepRV: Accelerating Spatiotemporal Inference with Pre-trained Neural Priors](https://mlsanity.com/paper/2503.21473/) (2025)
- [Scalable Bayesian Additive Models for Stellar Flare Detection via Amortized Gaussian Process Inference and Hidden Markov Models](https://mlsanity.com/paper/2606.22601/) (2026)

## Abstract (arXiv)

Recent advances have shown that GP priors, or their finite realisations, can be encoded using deep generative models such as variational autoencoders (VAEs). These learned generators can serve as drop-in replacements for the original priors during MCMC inference. While this approach enables efficient inference, it loses information about the hyperparameters of the original models, and consequently makes inference over hyperparameters impossible and the learned priors indistinct. To overcome this limitation, we condition the VAE on stochastic process hyperparameters. This allows the joint encoding of hyperparameters with GP realizations and their subsequent estimation during inference. Further, we demonstrate that our proposed method, PriorCVAE, is agnostic to the nature of the models which it approximates, and can be used, for instance, to encode solutions of ODEs. It provides a practical tool for approximate inference and shows potential in real-life spatial and spatiotemporal applications.