The Geometry of Phase Transitions in Generative Dynamics via Projection Caustics
Continuous-state generative samplers, including diffusion and flow-matching models, evolve through continuous reverse-time dynamics, yet their samples often undergo abrupt qualitative changes: trajectories commit to modes, semantic alternatives collapse, and small perturbations in narrow time windows can produce large downstream effects. This paper develops a geometric account of such phase-transition-like behaviour. We view denoising as gradient descent on a free energy landscape and show that sharp transitions arise near projection caustics, where the nearest-point projection onto the data support ceases to be unique. Motivated by this perspective, we introduce the Critical Boundary Det...
| Authors | Ryosuke Sakamoto, Kotaro Sakamoto |
|---|---|
| Primary category | cs.LG |
| Published | 11 June 2026 |
| Last updated at source | 11 June 2026 |
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