# Deterministic Langevin Monte Carlo with Normalizing Flows for Bayesian Inference

arXiv: https://arxiv.org/abs/2205.14240 · HTML: https://mlsanity.com/paper/2205.14240/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 44 references that are in the map.
- First posted on arXiv 27 May 2022.

## Builds on (most cited first, 14 of 14)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [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)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem](https://mlsanity.com/paper/1802.08089/) (2018)
- [Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2102.07501/) (2021)
- [Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation](https://mlsanity.com/paper/2006.00702/) (2020)
- [NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport](https://mlsanity.com/paper/1903.03704/) (2019)
- [On the Quantitative Analysis of Decoder-Based Generative Models](https://mlsanity.com/paper/1611.04273/) (2016)
- [Sliced Iterative Normalizing Flows](https://mlsanity.com/paper/2007.00674/) (2020)

## Built on by (most cited first, 10 of 10)

- [On Sampling with Approximate Transport Maps](https://mlsanity.com/paper/2302.04763/) (2023)
- [Can Microcanonical Langevin Dynamics Leverage Mini-Batch Gradient Noise?](https://mlsanity.com/paper/2602.06500/) (2026)
- [Mitigating mode collapse in normalizing flows by annealing with an adaptive schedule: Application to parameter estimation](https://mlsanity.com/paper/2505.03652/) (2025)
- [Learning Rate Free Sampling in Constrained Domains](https://mlsanity.com/paper/2305.14943/) (2023)
- [Mixed Variational Flows for Discrete Variables](https://mlsanity.com/paper/2308.15613/) (2023)
- [Hamiltonian Monte Carlo Inference of Marginalized Linear Mixed-Effects Models](https://mlsanity.com/paper/2410.24079/) (2024)
- [Empirical evaluation of normalizing flows in Markov Chain Monte Carlo](https://mlsanity.com/paper/2412.17136/) (2024)
- [Deterministic Langevin Unconstrained Optimization with Normalizing Flows](https://mlsanity.com/paper/2310.00745/) (2023)
- [Persistent Sampling: Enhancing the Efficiency of Sequential Monte Carlo](https://mlsanity.com/paper/2407.20722/) (2024)
- [Reducing normalizing flow complexity for MCMC preconditioning](https://mlsanity.com/paper/2511.02345/) (2025)

## Abstract (arXiv)

We propose a general purpose Bayesian inference algorithm for expensive likelihoods, replacing the stochastic term in the Langevin equation with a deterministic density gradient term. The particle density is evaluated from the current particle positions using a Normalizing Flow (NF), which is differentiable and has good generalization properties in high dimensions. We take advantage of NF preconditioning and NF based Metropolis-Hastings updates for a faster convergence. We show on various examples that the method is competitive against state of the art sampling methods.