From Hopfield Attractors to Diffusion Manifolds: Mapping Emergent Phases of Memorization

TL;DR: Let’s treat diffusion models like associative memory systems (think Hopfield networks) and see if we can systematically map and manipulate the emergence of “spurious states” as dataset size and training time vary.

Research Question: How do the attractor landscapes in diffusion models evolve across dataset regimes, and can we manipulate or visualize the emergence of memorization and spurious generalization states through associative memory theory?

Hypothesis: Diffusion models’ transition from memorization to generalization can be described and even predicted using associative memory theory; specifically, the density and stability of attractors (both true and spurious) will depend on training dynamics, and targeted interventions (e.g., noise injection, regularization) can shift these boundaries.

Experiment Plan: - Use techniques from Pham et al. (2025) to analyze attractor landscapes in trained diffusion models at various stages.

• Visualize basins of attraction and spurious states using dimensionality reduction and clustering in latent space.
• Experiment with interventions (e.g., regularization, dropout) and measure effects on attractor structure and memorization.
• Quantitatively relate the onset of spurious attractors to $\tau_\mathrm{mem}$ and dataset size.

References:

• Bonnaire, T., Urfin, R., Biroli, G., & M'ezard, M. (2025). Why Diffusion Models Don't Memorize: The Role of Implicit Dynamical Regularization in Training. arXiv.org.
• Pham, B., Raya, G., Negri, M., Zaki, M. J., Ambrogioni, L., & Krotov, D. (2025). Memorization to Generalization: Emergence of Diffusion Models from Associative Memory. arXiv.org.