# Rethinking the Diffusion Model from a Langevin Perspective

arXiv: https://arxiv.org/abs/2604.10465 · HTML: https://mlsanity.com/paper/2604.10465/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 7 of its 11 references that are in the map.
- First posted on arXiv 12 Apr 2026.

## Placed in

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

## Builds on (most cited first, 7 of 7)

- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [LanPaint: Training-Free Diffusion Inpainting with Asymptotically Exact and Fast Conditional Sampling](https://mlsanity.com/paper/2502.03491/) (2025)

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

- [Diffusion Editing with Soft Mask: Pixel Level Redo of Image and Video with Adjustable Strength](https://mlsanity.com/paper/2610.00359/) (2026)

## Abstract (arXiv)

Diffusion models are often introduced from multiple perspectives, such as VAEs, score matching, or flow matching, accompanied by dense and technically demanding mathematics that can be difficult for beginners to grasp. One classic question is: how does the reverse process invert the forward process to generate data from pure noise? This article systematically organizes the diffusion model from a fresh Langevin perspective, offering a simpler, clearer, and more intuitive answer. We also address the following questions: how can ODE-based and SDE-based diffusion models be unified under a single framework? Why are diffusion models theoretically superior to ordinary VAEs? Why is flow matching not fundamentally simpler than denoising or score matching, but equivalent under maximum-likelihood? We demonstrate that the Langevin perspective offers clear and straightforward answers to these questions, bridging existing interpretations of diffusion models, showing how different formulations can be converted into one another within a common framework, and offering pedagogical value for both learners and experienced researchers seeking deeper intuition.