Paper Overview
- Field: Computer Vision
- Authors: Danqi Zhuang, Jisui Huang, Xiaoyue Xi
- Published: 2025-06-06
- arXiv: 2506.04835
- The construction remains close to standard denoising diffusion models: for a periodically forced Ornstein-Uhlenbeck-type forward process, the authors derive:
- Closed-form forward marginal distributions
- A limiting periodic Gaussian terminal family
- Explicit Gaussian reverse posteriors, enabling standard noise-prediction training
- An invariant-mean regularization term couples phase-conditioned reverse dynamics through the mean of the periodic reference laws.
- Phase-conditioned error
- Feature-space covariance error
- Nearest-neighbor manifold distance
- arXiv: <https://arxiv.org/abs/2506.04835>
Summary
Standard diffusion models typically use a single time-homogeneous Gaussian terminal distribution as the reference law for generation. While analytically convenient and empirically powerful, this choice offers little explicit structure for data concentrated near low-dimensional manifolds, where different regions of the data distribution may correspond to distinct local geometric or semantic factors. As a result, the reverse model must recover manifold-level structure almost entirely from an unstructured terminal reference distribution.
The authors propose PTL-Diffusion, a proof-of-concept diffusion framework whose forward noising process converges to a nonconstant periodic family of Gaussian terminal laws rather than a single invariant law. Unlike phase-conditioned DDPM—where phase information only enters the denoising network while the forward process remains unchanged—PTL-Diffusion embeds phase structure directly into the forward noising dynamics.
Key contributions
Experimental results
On torus and cylinder point-cloud benchmarks and the Olivetti faces dataset, PTL-Diffusion improves manifold-level distribution matching and reduces: