# A theoretical basis for model collapse in recursive training

arXiv: https://arxiv.org/abs/2506.09401 · HTML: https://mlsanity.com/paper/2506.09401/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 15 references that are in the map.
- First posted on arXiv 11 Jun 2025.

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

- [The Curse of Recursion: Training on Generated Data Makes Models Forget](https://mlsanity.com/paper/2305.17493/) (2023)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data](https://mlsanity.com/paper/2404.01413/) (2024)
- [A Tale of Tails: Model Collapse as a Change of Scaling Laws](https://mlsanity.com/paper/2402.07043/) (2024)
- [Model Collapse Demystified: The Case of Regression](https://mlsanity.com/paper/2402.07712/) (2024)
- [Rate of Model Collapse in Recursive Training](https://mlsanity.com/paper/2412.17646/) (2024)
- [Heat Death of Generative Models in Closed-Loop Learning](https://mlsanity.com/paper/2404.02325/) (2024)

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

- [Adynamical systems view of training generativemodels and the memorization phenomenon](https://mlsanity.com/paper/2605.19483/) (2026)

## Abstract (arXiv)

It is known that recursive training from generative models can lead to the so called `collapse' of the simulated probability distribution. This note shows that one in fact gets two different asymptotic behaviours depending on whether an external source, howsoever minor, is also contributing samples.