# Stability and Diversity of Networked Self-Consuming Generative Ecosystems

arXiv: https://arxiv.org/abs/2610.09409 · HTML: https://mlsanity.com/paper/2610.09409/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 45 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Builds on (most cited first, 15 of 15)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Orca: Progressive Learning from Complex Explanation Traces of GPT-4](https://mlsanity.com/paper/2306.02707/) (2023)
- [The Curse of Recursion: Training on Generated Data Makes Models Forget](https://mlsanity.com/paper/2305.17493/) (2023)
- [Beyond Model Collapse: Scaling Up with Synthesized Data Requires Verification](https://mlsanity.com/paper/2406.07515/) (2024)
- [Self-Consuming Generative Models with Curated Data Provably Optimize Human Preferences](https://mlsanity.com/paper/2407.09499/) (2024)
- [Self-Correcting Self-Consuming Loops for Generative Model Training](https://mlsanity.com/paper/2402.07087/) (2024)
- [Self-Improving Diffusion Models with Synthetic Data](https://mlsanity.com/paper/2408.16333/) (2024)
- [Rate of Model Collapse in Recursive Training](https://mlsanity.com/paper/2412.17646/) (2024)
- [Self-Consuming Generative Models with Adversarially Curated Data](https://mlsanity.com/paper/2505.09768/) (2025)
- [What happens when generative AI models train recursively on each others' outputs?](https://mlsanity.com/paper/2505.21677/) (2025)
- [Escaping Model Collapse via Synthetic Data Verification: Near-term Improvements and Long-term Convergence](https://mlsanity.com/paper/2510.16657/) (2025)
- [Stabilizing Self-Consuming Diffusion Models with Latent Space Filtering](https://mlsanity.com/paper/2511.12742/) (2025)
- [Convergence Dynamics and Stabilization Strategies of Co-Evolving Generative Models](https://mlsanity.com/paper/2503.08117/) (2025)
- [When and How Human Curation Backfires: Preference Alignment under Multi-Model Self-Consuming Loop](https://mlsanity.com/paper/2605.29267/) (2026)

## Abstract (arXiv)

The widespread deployment of generative AI has made it increasingly difficult to distinguish synthetic content from real data. Consequently, synthetic data is inevitably incorporated into the training pipelines of future model generations, forming a self-consuming training loop. Prior work has studied the effects of such recursive self-consuming training, but analyses have largely been limited to isolated models, where a model consumes only its own synthetic data, or to simplified interactions between two models. This paper takes a first step toward understanding networked self-consuming generative models, in which multiple models consume synthetic data generated by one another through complex interaction pathways. We introduce a theoretical framework representing models as nodes in a directed, weighted graph, with edge weights governing the flow of synthetic data among models. Using this framework, we analyze the long-term behavior of networked models under retraining dynamics, establishing conditions for convergence and characterizing the resulting fixed points. We further investigate how the system's long-term stability and diversity are shaped by each model's access to real data, cross-model data consumption, and the structure of the interaction graph.