Understanding Deterministic Diffusion through Reverse Transition Kernels

Adrita Das, Peiran Jiang, Dantong Zhu, Barnabas Poczos, Jose Lugo-Martinez

Keywords: Diffusion Models; Deterministic Diffusion; Directly Denoising Diffusion Models (DDDM); Reverse Transition Kernel (RTK)

Abstract:

Diffusion models have become a leading paradigm for generative modeling across both visual and scientific domains; however, their widespread deployment is fundamentally constrained by the high computational cost of sampling, which typically requires long stochastic trajectories and sequential updates. This bottleneck is particularly pronounced in high-dimensional settings such as molecular generation and image synthesis, where inference latency scales poorly with both dimensionality and the number of diffusion steps. Our work provides a principled foundation for overcoming this limitation by showing that deterministic diffusion models, when viewed through the Reverse Transition Kernel (RTK) framework (Huang et al. (2024)), induce structured and well-conditioned reverse-time subproblems. This perspective suggests that the sampling process can be interpreted as a sequence of approximately strongly log-concave optimization problems, which in turn facilitates stable updates and supports the use of constant step sizes in practice. Beyond theoretical implications, this reinterpretation provides a unifying lens for understanding deterministic and stochastic diffusion, while offering a practical pathway toward fast, stable, and scalable generative modeling. We further provide empirical validation of our theoretical analysis by measuring
key regularity properties of the learned denoiser. On molecular benchmarks, our method achieves faster convergence and improved structural fidelity while preserving chemical validity. On image generation tasks, we observe consistent gains in stability and sample quality, supporting the generality of the framework. These findings suggest a promising pathway toward scalable and efficient sampling of
high-dimensional data.

Submission Number: 136