Neural Bridge Processes Improve Input Conditioning in Diffusion Models

A novel machine learning approach known as Neural Bridge Processes (NBPs) substitutes the input-independent forward kernel found in Neural Diffusion Processes (NDPs) with a bridge trajectory that is anchored to the input. This innovation enables the encoding of conditioning inputs in noisy training states, enhancing both expressivity and uncertainty-aware learning from partially observed context-target pairs. In scenarios where input and output dimensions are not aligned, NBPs establish an output-space anchor a_ψ(x)=P_ψ(x) to direct the generative trajectory while preserving the integrity of the denoising backbone. Theoretical evaluations indicate that process-level anchoring promotes pathwise input distinguishability, infuses noisy states with information about x, and establishes a direct gradient pathway. The research can be accessed on arXiv under ID 2508.07220.