mlsanityData to 14 Oct 2026

Neural Bridge Processes

arXiv 2508.07220 ↗First posted 10 Aug 2025cs.LG cs.AIcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 49 of its 63 references that are in the map. First posted on arXiv 10 Aug 2025.

Builds on

49 of 63 references.

Closest ancestors · 19

Same direction, newest first

  1. 2025Constrained Generative Modeling with Manually Bridged Diffusion Models27 Feb
  2. 2024Consistency Diffusion Bridge Models30 Oct
  3. 2024Sparse Inducing Points in Deep Gaussian Processes: Enhancing Modeling with Denoising Diffusion Variational Inference24 Jul
  4. 2024Diffusion Bridge Implicit Models24 May
  5. 2023Denoising Diffusion Bridge Models29 Sep
  6. 2023Geometric Neural Diffusion Processes11 Jul
  7. 2023SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis4 Jul
  8. 2023Diffusion Models for Black-Box Optimization12 Jun
  9. 2023Diffusion Schr"odinger Bridge Matching29 Mar
  10. 2023Continuous-Time Functional Diffusion Processes1 Mar
  11. 2022Scalable Diffusion Models with Transformers19 Dec
  12. 2022Diffusion Models in Vision: A Survey10 Sep
7 more
  1. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  2. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models6 Aug
  3. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matching5 Jun
  4. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  5. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  6. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  7. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 30

  1. 2022Flow Matching for Generative Modelingcited by 5,702
  2. 2023Adding Conditional Control to Text-to-Image Diffusion Modelscited by 5,503
  3. 2018Neural Ordinary Differential Equationscited by 3,779
  4. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,430
  5. 2014Deep Learning in Neural Networks: An Overviewcited by 770
  6. 2021A Survey of Uncertainty in Deep Neural Networkscited by 680
  7. 2015Deep Kernel Learningcited by 445
  8. 2018Conditional Neural Processescited by 426
  9. 2018Neural Processescited by 311
  10. 2019Attentive Neural Processescited by 283
  11. 2022BBDM: Image-to-image Translation with Brownian Bridge Diffusion Modelscited by 225
  12. 2019Convolutional Conditional Neural Processescited by 142
18 more
  1. 2022Transformer Neural Processes: Uncertainty-Aware Meta Learning Via Sequence Modelingcited by 127
  2. 2018Uncertainty in Neural Networks: Approximately Bayesian Ensemblingcited by 94
  3. 2023Diffusion Bridge Mixture Transports, Schr"odinger Bridge Problems and Generative Modelingcited by 80
  4. 2020Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processescited by 76
  5. 2023Conditional Text Image Generation with Diffusion Modelscited by 58
  6. 2021Neural ODE Processescited by 57
  7. 2019Sequential Neural Processescited by 55
  8. 2024LLM Processes: Numerical Predictive Distributions Conditioned on Natural Languagecited by 55
  9. 2022Neural Diffusion Processescited by 50
  10. 2019The Functional Neural Processcited by 43
  11. 2023Image Restoration Through Generalized Ornstein-Uhlenbeck Bridgecited by 41
  12. 2021The Gaussian Neural Processcited by 34
  13. 2023Autoregressive Conditional Neural Processescited by 33
  14. 2024Amortized Probabilistic Conditioning for Optimization, Simulation and Inferencecited by 23
  15. 2023Graph Neural Processes for Spatio-Temporal Extrapolationcited by 19
  16. 2023Sparse Variational Student-t Processescited by 8
  17. 2020Deep Latent-Variable Kernel Learningcited by 5
  18. 2023Diffusion-Augmented Neural Processescited by 2

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  1. 2025Neural Guided Diffusion Bridges
  2. 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling
  3. 2026GuidedBridge: Training-freely Improving Bridge Models with Prior Guidance
  4. 2023Augmented Bridge Matching
  5. 2025On Approaches to Building Surrogate ODE Models for Diffusion Bridges
  6. 2026Rethinking Flow and Diffusion Bridge Models for Speech Enhancement
  7. 2025Sample from What You See: Visuomotor Policy Learning via Diffusion Bridge with Observation-Embedded Stochastic Differential Equation
  8. 2024Diffusion Tuning: Transferring Diffusion Models via Chain of Forgetting