Beyond Fixed Horizons: A Theoretical Framework for Adaptive Denoising Diffusions

Akeylimitationofthesemodels,however,istheirrelianceon a fixed time horizon, which introduces an artificial time dependency in the drift function of the backward process. As a result, the generative denoising process follows a predefined number of steps, regardless of the actual level of noise present along the generated path. To overcome this limitation, we introduce a novel class of diffusion models that dynamically adapt to the state of the denoising process. By replacing the fixed deterministic time horizon with a random one and conditioning the forward process to terminate at a predefined target distribution, our approach achieves greater flexibility and state awareness. The foundation of our method lies in Doob's h-transforms with respect to underlying exponential times. While the theoretical groundwork for this concept exists, its explicit application and detailed exploration - particularly in comparison to deterministic time horizons - remains underrepresented in the literature. A key feature of our model is its inherent adaptability: the number of denoising steps dynamically adjusts based on the noise level in the data, introducing a stochastic element. This randomness not only enhances the generation process, but also allows denoising to start from partially noisy data, naturally incorporating conditioning.