Connects DDIM reverse chains to fractal geometry, providing a mathematical explanation for why diffusion models switch from global context to local detail.
arXiv · March 16, 2026 · 2603.13069
Why it matters
It replaces empirical trial-and-error in diffusion design with explicit geometric optimization problems, deriving optimal schedules and SNR shifts mathematically rather than through exhaustive sweeps.
From the abstract
What is a diffusion model actually doing when it turns noise into a photograph?We show that the deterministic DDIM reverse chain operates as a Partitioned Iterated Function System (PIFS) and that this framework serves as a unified design language for denoising diffusion model schedules, architectures, and training objectives. From the PIFS structure we derive three computable geometric quantities: a per-step contraction threshold $L^*_t$, a diagonal expansion function $f_t(\lambda)$ and a global