# Amortized Inference of Multi-Modal Posteriors using Likelihood-Weighted Normalizing Flows

arXiv: https://arxiv.org/abs/2512.04954 · HTML: https://mlsanity.com/paper/2512.04954/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 42 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Builds on (most cited first, 18 of 18)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [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)
- [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)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [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)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Flow Annealed Importance Sampling Bootstrap](https://mlsanity.com/paper/2208.01893/) (2022)
- [normflows: A PyTorch Package for Normalizing Flows](https://mlsanity.com/paper/2302.12014/) (2023)
- [Emerging Convolutions for Generative Normalizing Flows](https://mlsanity.com/paper/1901.11137/) (2019)
- [Constraining Effective Field Theories with Machine Learning](https://mlsanity.com/paper/1805.00013/) (2018)
- [On the Need for Topology-Aware Generative Models for Manifold-Based Defenses](https://mlsanity.com/paper/1909.03334/) (2019)
- [Enhancing anomaly detection with topology-aware autoencoders](https://mlsanity.com/paper/2502.10163/) (2025)

## Abstract (arXiv)

We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling. This approach allows for the efficient inference of theoretical parameters in high-dimensional inverse problems without the need for posterior training samples. We implement the method on multi-modal benchmark tasks in 2D and 3D to check for the efficacy. A critical observation of our study is the impact of the topology of the base distributions on the modelled posteriors. We find that standard unimodal base distributions fail to capture disconnected support, resulting in spurious probability textitbridges between modes. We demonstrate that initializing the flow with a Gaussian Mixture Model that matches the cardinality of the target modes significantly improves reconstruction fidelity, as measured by some distance and divergence metrics. Finally, we apply this method to a curated problem in heavy flavour physics --- the extraction of the Wolfenstein parameters from the CP asymmetry in B0→ J/psi,K0; it is multimodal, non-Gaussian, and asymmetric in its mode weights --- and compare the results against a well-converged Markov Chain Monte Carlo reference using different metrics.