# Dynamical Regimes of Multimodal Diffusion Models

arXiv: https://arxiv.org/abs/2602.04780 · HTML: https://mlsanity.com/paper/2602.04780/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 28 of its 47 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models](https://mlsanity.com/paper/2406.08070/) (2024)
- [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024)
- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [Spontaneous Symmetry Breaking in Generative Diffusion Models](https://mlsanity.com/paper/2305.19693/) (2023)
- [The Principles of Diffusion Models](https://mlsanity.com/paper/2510.21890/) (2025)
- [The statistical thermodynamics of generative diffusion models: Phase transitions, symmetry breaking and critical instability](https://mlsanity.com/paper/2310.17467/) (2023)
- [Analysis of learning a flow-based generative model from limited sample complexity](https://mlsanity.com/paper/2310.03575/) (2023)
- [Nonequilbrium physics of generative diffusion models](https://mlsanity.com/paper/2405.11932/) (2024)

## Built on by (most cited first, 4 of 4)

- [Steering Dynamical Regimes of Diffusion Models by Breaking Detailed Balance](https://mlsanity.com/paper/2602.15914/) (2026)
- [Is Your Diffusion Sampler Actually Correct? A Sampler-Centric Evaluation of Discrete Diffusion Language Models](https://mlsanity.com/paper/2602.19619/) (2026)
- [Interpreting the Synchronization Gap: The Hidden Mechanism Inside Diffusion Transformers](https://mlsanity.com/paper/2603.20987/) (2026)
- [Posterior Information Dynamics of Diffusion Models for Linear Inverse Problems](https://mlsanity.com/paper/2608.21709/) (2026)

## Abstract (arXiv)

Diffusion based generative models have achieved unprecedented fidelity in synthesizing high dimensional data, yet the theoretical mechanisms governing multimodal generation remain poorly understood. Here, we present a theoretical framework for coupled diffusion models, using coupled Ornstein-Uhlenbeck processes as a tractable model. By using the nonequilibrium statistical physics of dynamical phase transitions, we demonstrate that multimodal generation is governed by a spectral hierarchy of interaction timescales rather than simultaneous resolution. A key prediction is the ``synchronization gap'', a temporal window during the reverse generative process where distinct eigenmodes stabilize at different rates, providing a theoretical explanation for common desynchronization artifacts. We derive analytical conditions for speciation and collapse times under both symmetric and anisotropic coupling regimes, establishing strict bounds for coupling strength to avoid unstable symmetry breaking. We show that the coupling strength acts as a spectral filter that enforces a tunable temporal hierarchy on generation. We support these predictions through controlled experiments with diffusion models trained on MNIST datasets and exact score samplers. These results motivate time dependent coupling schedules that target mode specific timescales, offering a potential alternative to ad hoc guidance tuning.