Search papers, labs, and topics across Lattice.
This paper analyzes the role of time conditioning in diffusion models from a geometric perspective, arguing that successful generation depends on disentangling noisy data manifolds in high-dimensional space. They modify the DDIM forward process to align the noisy data manifold with flow matching, demonstrating that DDIM can generate high-quality content without time conditioning. They further extend this framework to class-conditioned generation by decoupling classes into distinct time spaces, enabling class-conditional synthesis with a class-unconditional denoising model.
Time conditioning, a seemingly crucial component of diffusion models like DDIM, can be entirely bypassed without sacrificing generation quality by carefully shaping the evolution of noisy data manifolds.
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.
