# Diffusion Density Estimators

arXiv: https://arxiv.org/abs/2410.06986 · HTML: https://mlsanity.com/paper/2410.06986/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 9 Oct 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 12 of 12)

- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Your Diffusion Model is Secretly a Zero-Shot Classifier](https://mlsanity.com/paper/2303.16203/) (2023)
- [A Variational Perspective on Diffusion-Based Generative Models and Score Matching](https://mlsanity.com/paper/2106.02808/) (2021)
- [Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation](https://mlsanity.com/paper/2006.00702/) (2020)
- [Estimating the Spectral Density of Large Implicit Matrices](https://mlsanity.com/paper/1802.03451/) (2018)
- [Generative Diffusion From An Action Principle](https://mlsanity.com/paper/2310.04490/) (2023)

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

- [RNE: plug-and-play diffusion inference-time control and energy-based training](https://mlsanity.com/paper/2506.05668/) (2025)
- [Comparing Normalizing Flows with Kernel Density Estimation in Estimating Risk of Automated Driving Systems](https://mlsanity.com/paper/2507.22429/) (2025)

## Abstract (arXiv)

We investigate the use of diffusion models as neural density estimators. The current approach to this problem involves converting the generative process to a smooth flow, known as the Probability Flow ODE. The log density at a given sample can be obtained by solving the ODE with a black-box solver. We introduce a new, highly parallelizable method that computes log densities without the need to solve a flow. Our approach is based on estimating a path integral by Monte Carlo, in a manner identical to the simulation-free training of diffusion models. We also study how different training parameters affect the accuracy of the density calculation, and offer insights into how these models can be made more scalable and efficient.