# Quantifying the Ease of Reproducing Training Data in Unconditional Diffusion Models

arXiv: https://arxiv.org/abs/2503.19429 · HTML: https://mlsanity.com/paper/2503.19429/

## 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 9 of its 18 references that are in the map.
- First posted on arXiv 25 Mar 2025.

## Placed in

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

## Builds on (most cited first, 9 of 9)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Models](https://mlsanity.com/paper/2212.03860/) (2022)
- [Understanding and Mitigating Copying in Diffusion Models](https://mlsanity.com/paper/2305.20086/) (2023)
- [Estimating High Order Gradients of the Data Distribution by Denoising](https://mlsanity.com/paper/2111.04726/) (2021)

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

- [Diffusion Models Memorize in Training -- and Generalize in Inference](https://mlsanity.com/paper/2603.13419/) (2026)

## Abstract (arXiv)

Diffusion models, which have been advancing rapidly in recent years, may generate samples that closely resemble the training data. This phenomenon, known as memorization, may lead to copyright issues. In this study, we propose a method to quantify the ease of reproducing training data in unconditional diffusion models. The average of a sample population following the Langevin equation in the reverse diffusion process moves according to a first-order ordinary differential equation (ODE). This ODE establishes a 1-to-1 correspondence between images and their noisy counterparts in the latent space. Since the ODE is reversible and the initial noisy images are sampled randomly, the volume of an image's projected area represents the probability of generating those images. We examined the ODE, which projects images to latent space, and succeeded in quantifying the ease of reproducing training data by measuring the volume growth rate in this process. Given the relatively low computational complexity of this method, it allows us to enhance the quality of training data by detecting and modifying the easily memorized training samples.