Exploring Time Conditioning in Diffusion Generative Models from Disjoint Noisy Data Manifolds

TL;DR

This paper demonstrates that high-quality diffusion model generation can occur without explicit time conditioning by analyzing the geometric structure of noisy data manifolds and modifying the forward diffusion process.

Contribution

The authors show that DDIM can generate high-quality content without time conditioning by aligning the noisy data manifold with flow-matching methods, extending to class-conditioned generation.

Findings

DDIM can produce high-quality samples without time conditioning.

Noisy data distributions concentrate on low-dimensional manifolds in high-dimensional space.

Modifying the forward process to match flow-matching enables unconditional generation.

Abstract

Practically, training diffusion models typically requires explicit time conditioning to guide the network through the denoising sampling process. Especially in deterministic methods like DDIM, the absence of time conditioning leads to significant performance degradation. However, other deterministic sampling approaches, such as flow matching, can generate high-quality content without this conditioning, raising the question of its necessity. In this work, we revisit the role of time conditioning from a geometric perspective. We analyze the evolution of noisy data distributions under the forward diffusion process and demonstrate that, in high-dimensional spaces, these distributions concentrate on low-dimensional hyper-cylinder-like manifolds embedded within the input space. Successful generation, we argue, stems from the disentanglement of these manifolds in high-dimensional space. Based on this insight, we modify the forward process of DDIM to align the noisy data manifold with the flow-matching approach, proving that DDIM can generate high-quality content without time conditioning, provided the noisy manifold evolves according to the flow-matching method. Additionally, we extend our framework to class-conditioned generation by decoupling classes into distinct time spaces, enabling class-conditioned synthesis with a class-unconditional denoising model. Extensive experiments validate our theoretical analysis and show that high-quality generation is achievable without explicit conditional embeddings.