# Improving the evaluation of samplers on multi-modal targets

arXiv: https://arxiv.org/abs/2504.08916 · HTML: https://mlsanity.com/paper/2504.08916/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 52 references that are in the map.
- First posted on arXiv 11 Apr 2025.

## Builds on (most cited first, 28 of 28)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Theoretical guarantees for approximate sampling from smooth and log-concave densities](https://mlsanity.com/paper/1412.7392/) (2014)
- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Denoising Diffusion Samplers](https://mlsanity.com/paper/2302.13834/) (2023)
- [An optimal control perspective on diffusion-based generative modeling](https://mlsanity.com/paper/2211.01364/) (2022)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [Log-concave sampling: Metropolis-Hastings algorithms are fast](https://mlsanity.com/paper/1801.02309/) (2018)
- [Improved sampling via learned diffusions](https://mlsanity.com/paper/2307.01198/) (2023)
- [normflows: A PyTorch Package for Normalizing Flows](https://mlsanity.com/paper/2302.12014/) (2023)
- [Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Sampling](https://mlsanity.com/paper/2406.07423/) (2024)
- [Sequential Controlled Langevin Diffusions](https://mlsanity.com/paper/2412.07081/) (2024)
- [Learning Interpolations between Boltzmann Densities](https://mlsanity.com/paper/2301.07388/) (2023)
- [Reverse Diffusion Monte Carlo](https://mlsanity.com/paper/2307.02037/) (2023)
- [Sampling, Diffusions, and Stochastic Localization](https://mlsanity.com/paper/2305.10690/) (2023)
- [Coupling and Convergence for Hamiltonian Monte Carlo](https://mlsanity.com/paper/1805.00452/) (2018)
- [Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors](https://mlsanity.com/paper/2006.12335/) (2020)
- [Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence](https://mlsanity.com/paper/2106.15980/) (2021)
- [Stochastic Localization via Iterative Posterior Sampling](https://mlsanity.com/paper/2402.10758/) (2024)
- [On Sampling with Approximate Transport Maps](https://mlsanity.com/paper/2302.04763/) (2023)
- [Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusion](https://mlsanity.com/paper/2402.17886/) (2024)
- [Faster Sampling without Isoperimetry via Diffusion-based Monte Carlo](https://mlsanity.com/paper/2401.06325/) (2024)
- [A theoretical perspective on mode collapse in variational inference](https://mlsanity.com/paper/2410.13300/) (2024)
- [Learned Reference-based Diffusion Sampling for multi-modal distributions](https://mlsanity.com/paper/2410.19449/) (2024)
- [Fighting Sample Degeneracy and Impoverishment in Particle Filters: A Review of Intelligent Approaches](https://mlsanity.com/paper/1308.2443/) (2013)

## Built on by (most cited first, 9 of 9)

- [Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference](https://mlsanity.com/paper/2508.12511/) (2025)
- [Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching](https://mlsanity.com/paper/2603.00530/) (2026)
- [Annealing in variational inference mitigates mode collapse: A theoretical study on Gaussian mixtures](https://mlsanity.com/paper/2602.12923/) (2026)
- [Exact Global MCMC with Denoising Diffusion](https://mlsanity.com/paper/2609.00279/) (2026)
- [The critical slowing down in training diffusion models](https://mlsanity.com/paper/2605.12597/) (2026)
- [Particle Monte Carlo methods for Lattice Field Theory](https://mlsanity.com/paper/2511.15196/) (2025)
- [Sampling from multi-modal distributions on Riemannian manifolds with training-free stochastic interpolants](https://mlsanity.com/paper/2602.00641/) (2026)
- [Entropic Mirror Monte Carlo](https://mlsanity.com/paper/2602.03165/) (2026)
- [Total Variation Guarantees for Sampling with Stochastic Localization](https://mlsanity.com/paper/2603.29555/) (2026)

## Abstract (arXiv)

Addressing multi-modality constitutes one of the major challenges of sampling. In this reflection paper, we advocate for a more systematic evaluation of samplers towards two sources of difficulty that are mode separation and dimension. For this, we propose a synthetic experimental setting that we illustrate on a selection of samplers, focusing on the challenging criterion of recovery of the mode relative importance. These evaluations are crucial to diagnose the potential of samplers to handle multi-modality and therefore to drive progress in the field.