Title: Neural  Bridge Processes
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: Neural Processes, Diffusion Bridge, functions learning

Abstract: Learning stochastic functions from partially observed context-target pairs is a fundamental problem in probabilistic modeling. Traditional models like Gaussian Processes (GPs) face scalability issues with large datasets and assume Gaussianity, limiting their applicability. While Neural Processes (NPs) offer more flexibility, they struggle with capturing complex, multi-modal target distributions. Neural Diffusion Processes (NDPs) enhance expressivity through a learned diffusion process but rely solely on conditional signals in the denoising network, resulting in weak input coupling from an unconditional forward process and semantic mismatch at the diffusion endpoint. In this work, we propose Neural  Bridge Processes (NBPs), a novel method for modeling stochastic functions where inputs \( x \) act as dynamic anchors for the entire diffusion trajectory. By reformulating the forward kernel to explicitly depend on \( x \), NBP enforces a constrained path that strictly terminates at the supervised target. This approach not only provides stronger gradient signals but also guarantees endpoint coherence. We validate NBPs on synthetic data, EEG signal regression and image regression tasks, achieving substantial improvements over baselines. These results underscore the effectiveness of DDPM-style bridge sampling in enhancing both performance and theoretical consistency for structured prediction tasks.