# Diffusion-based supervised learning of generative models for efficient sampling of multimodal distributions

arXiv: https://arxiv.org/abs/2505.07825 · HTML: https://mlsanity.com/paper/2505.07825/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 31 references that are in the map.
- First posted on arXiv 20 Apr 2025.

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Stochastic Normalizing Flows](https://mlsanity.com/paper/2002.06707/) (2020)
- [Dynamic nested sampling: an improved algorithm for parameter estimation and evidence calculation](https://mlsanity.com/paper/1704.03459/) (2017)
- [Diffusion-Model-Assisted Supervised Learning of Generative Models for Density Estimation](https://mlsanity.com/paper/2310.14458/) (2023)
- [Warp Bridge Sampling: The Next Generation](https://mlsanity.com/paper/1609.07690/) (2016)

## Built on by (most cited first, 2 of 2)

- [Gradient-Informed Monte Carlo Fine-Tuning of Diffusion Models for Low-Thrust Trajectory Design](https://mlsanity.com/paper/2512.08705/) (2025)
- [Nonlocal Hamiltonian Dynamics on Sparse L'evy Graphs: Spectral Analysis and Multimodal Sampling](https://mlsanity.com/paper/2610.06904/) (2026)

## Abstract (arXiv)

We propose a hybrid generative model for efficient sampling of high-dimensional, multimodal probability distributions for Bayesian inference. Traditional Monte Carlo methods, such as the Metropolis-Hastings and Langevin Monte Carlo sampling methods, are effective for sampling from single-mode distributions in high-dimensional spaces. However, these methods struggle to produce samples with the correct proportions for each mode in multimodal distributions, especially for distributions with well separated modes. To address the challenges posed by multimodality, we adopt a divide-and-conquer strategy. We start by minimizing the energy function with initial guesses uniformly distributed within the prior domain to identify all the modes of the energy function. Then, we train a classifier to segment the domain corresponding to each mode. After the domain decomposition, we train a diffusion-model-assisted generative model for each identified mode within its support. Once each mode is characterized, we employ bridge sampling to estimate the normalizing constant, allowing us to directly adjust the ratios between the modes. Our numerical examples demonstrate that the proposed framework can effectively handle multimodal distributions with varying mode shapes in up to 100 dimensions. An application to Bayesian inverse problem for partial differential equations is also provided.