# Normalizing Flow Regression for Bayesian Inference with Offline Likelihood Evaluations

arXiv: https://arxiv.org/abs/2504.11554 · HTML: https://mlsanity.com/paper/2504.11554/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 68 references that are in the map.
- First posted on arXiv 15 Apr 2025.

## Builds on (most cited first, 30 of 31)

- [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)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Yes, but Did It Work?: Evaluating Variational Inference](https://mlsanity.com/paper/1802.02538/) (2018)
- [Pareto Smoothed Importance Sampling](https://mlsanity.com/paper/1507.02646/) (2015)
- [Resampling Base Distributions of Normalizing Flows](https://mlsanity.com/paper/2110.15828/) (2021)
- [Advances in Black-Box VI: Normalizing Flows, Importance Weighting, and Optimization](https://mlsanity.com/paper/2006.10343/) (2020)
- [Challenges and Opportunities in High-dimensional Variational Inference](https://mlsanity.com/paper/2103.01085/) (2021)
- [Sampling for Inference in Probabilistic Models with Fast Bayesian Quadrature](https://mlsanity.com/paper/1411.0439/) (2014)
- [Variational Bayesian Monte Carlo with Noisy Likelihoods](https://mlsanity.com/paper/2006.08655/) (2020)
- [Prior knowledge elicitation: The past, present, and future](https://mlsanity.com/paper/2112.01380/) (2021)
- [Variational Bayesian Monte Carlo](https://mlsanity.com/paper/1810.05558/) (2018)
- [Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination](https://mlsanity.com/paper/2206.04734/) (2022)
- [Parallel Gaussian process surrogate Bayesian inference with noisy likelihood evaluations](https://mlsanity.com/paper/1905.01252/) (2019)
- [Practical Bayesian Optimization for Model Fitting with Bayesian Adaptive Direct Search](https://mlsanity.com/paper/1705.04405/) (2017)
- [Parallel MCMC Without Embarrassing Failures](https://mlsanity.com/paper/2202.11154/) (2022)
- [Variational Inference with NoFAS: Normalizing Flow with Adaptive Surrogate for Computationally Expensive Models](https://mlsanity.com/paper/2108.12657/) (2021)
- [PyVBMC: Efficient Bayesian inference in Python](https://mlsanity.com/paper/2303.09519/) (2023)
- [Fast and robust Bayesian Inference using Gaussian Processes with GPry](https://mlsanity.com/paper/2211.02045/) (2022)
- [Unbiased and Efficient Log-Likelihood Estimation with Inverse Binomial Sampling](https://mlsanity.com/paper/2001.03985/) (2020)
- [Fast post-process Bayesian inference with Variational Sparse Bayesian Quadrature](https://mlsanity.com/paper/2303.05263/) (2023)

## Built on by (most cited first, 1 of 1)

- [Mode Collapse Is Cheap to Detect: A Ground-Truth-Free Pre-Flight Check for Neural Samplers](https://mlsanity.com/paper/2609.26272/) (2026)

## Abstract (arXiv)

Bayesian inference with computationally expensive likelihood evaluations remains a significant challenge in many scientific domains. We propose normalizing flow regression (NFR), a novel offline inference method for approximating posterior distributions. Unlike traditional surrogate approaches that require additional sampling or inference steps, NFR directly yields a tractable posterior approximation through regression on existing log-density evaluations. We introduce training techniques specifically for flow regression, such as tailored priors and likelihood functions, to achieve robust posterior and model evidence estimation. We demonstrate NFR's effectiveness on synthetic benchmarks and real-world applications from neuroscience and biology, showing superior or comparable performance to existing methods. NFR represents a promising approach for Bayesian inference when standard methods are computationally prohibitive or existing model evaluations can be recycled.