aiqbench analysis
Neural Bridge Processes introduce a novel input-anchored mechanism for stochastic function modeling, addressing the limitation in Neural Diffusion Processes where conditioning information fails to propagate through the forward process. By creating a direct gradient pathway and enabling coordinates to guide generative paths, this method significantly enhances expressivity and uncertainty awareness across diverse tasks like EEG analysis and image regression. The findings suggest that bridge-anchored trajectories offer a robust generalization for strengthening conditional modeling in complex stochastic systems.
Neural Bridge Processes
arXiv:2508.07220v4 Announce Type: replace Abstract: Learning stochastic functions from partially observed context-target pairs requires models that are expressive, uncertainty-aware, and strongly conditioned on inputs. Neural Diffusion Processes (NDPs) improve expressivity with denoising diffusion, but their forward process is input-independent; inputs only enter the reverse denoiser, so the noisy training states themselves do not encode the conditioning inputs. We propose Neural Bridge Processes (NBPs), which replace the unconditional forward kernel with an input-anchored bridge trajectory. When input and output dimensions differ, NBP learns an output-space anchor $a_\psi(x)=P_\psi(x)$, allowing coordinates or other inputs to guide the generative path without changing the denoising backbone. We show theoretically that process-level anchoring induces pathwise input distinguishability, injects information about x into noisy states, and creates a direct gradient pathway unavailable to NDPs. Experiments on synthetic regression, EEG, CylinderFlow, and image regression show consistent improvements. Additional ablations show that the gains come from the full bridge construction with learned alignment, and that the same input-anchored path principle transfers to Flow Matching Neural Processes. These results suggest that bridge-anchored generative paths provide a general mechanism for strengthening conditional stochastic function modeling.
Abstract:Learning stochastic functions from partially observed context-target pairs requires models that are expressive, uncertainty-aware, and strongly conditioned on inputs. Neural Diffusion Processes (NDPs) improve expressivity with denoising diffusion, but their forward process is input-independent; inputs only enter the reverse denoiser, so the noisy training states themselves do not encode the conditioning inputs. We propose Neural Bridge Processes (NBPs), which replace the unconditional forward kernel with an input-anchored bridge trajectory. When input and output dimensions differ, NBP learns an output-space anchor $a_\psi(x)=P_\psi(x)$, allowing coordinates or other inputs to guide the generative path without changing the denoising backbone. We show theoretically that process-level anchoring induces pathwise input distinguishability, injects information about x into noisy states, and creates a direct gradient pathway unavailable to NDPs. Experiments on synthetic regression, EEG, CylinderFlow, and image regression show consistent improvements. Additional ablations show that the gains come from the full bridge construction with learned alignment, and that the same input-anchored path principle transfers to Flow Matching Neural Processes. These results suggest that bridge-anchored generative paths provide a general mechanism for strengthening conditional stochastic function modeling.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2508.07220 [cs.LG]
(or arXiv:2508.07220v4 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2508.07220 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 274 words
