# A Novel Framework Using Variational Inference with Normalizing Flows to Train Transport Reversible Jump Proposals

arXiv: https://arxiv.org/abs/2512.12742 · HTML: https://mlsanity.com/paper/2512.12742/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 31 references that are in the map.
- First posted on arXiv 14 Dec 2025.

## Builds on (most cited first, 10 of 10)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport](https://mlsanity.com/paper/1903.03704/) (2019)
- [Representational aspects of depth and conditioning in normalizing flows](https://mlsanity.com/paper/2010.01155/) (2020)
- [Efficient Bayesian Sampling Using Normalizing Flows to Assist Markov Chain Monte Carlo Methods](https://mlsanity.com/paper/2107.08001/) (2021)
- [Transport Reversible Jump Proposals](https://mlsanity.com/paper/2210.12572/) (2022)
- [Informed reversible jump algorithms](https://mlsanity.com/paper/1911.02089/) (2019)

## Abstract (arXiv)

We propose a unified framework that employs variational inference (VI) with (conditional) normalizing flows (NFs) to train both between-model and within-model proposals for reversible jump Markov chain Monte Carlo, enabling efficient trans-dimensional Bayesian inference. In contrast to the transport reversible jump (TRJ) of Davies et al. (2023), which optimizes forward KL divergence using pilot samples from the complex target distribution, our approach minimizes the reverse KL divergence, requiring only samples from a simple base distribution and largely reducing computational cost. Especially, we develop a novel trans-dimensional VI method with conditional NFs to fit the conditional transport proposal of Davies et al. (2023). We use RealNVP flows to learn the model-specific transport maps used for constructing proposals so that the calculation is parallelizable. Our framework also provides accurate estimates of marginal likelihoods, which may facilitate efficient model comparison and help design rejection-free proposals. Extensive numerical studies demonstrate that the TRJ method trained under our framework achieves faster mixing compared to existing baselines.