In plain words: A generator can move noise toward real data along a random path pinned to hit the target distribution at fixed times. Gaussian versions of these paths produced high-quality samples in far fewer steps than usual step-by-step samplers, with similar image-quality scores.
Abstract
This paper motivates the use of random-bridges -- stochastic processes conditioned to take target distributions at fixed timepoints -- in the realm of generative modelling. Herein, random-bridges can act as stochastic transports between two probability distributions when appropriately initialized, and can display either Markovian or non-Markovian, and either continuous, discontinuous or hybrid patterns depending on the driving process. We show how one can start from general probabilistic statements and then branch out into specific representations for learning and simulation algorithms in terms of information processing. Our empirical results, built on Gaussian random bridges, produce high-quality samples in significantly fewer steps compared to traditional approaches, while achieving competitive Frechet inception distance scores. Our analysis provides evidence that the proposed framework is computationally cheap and suitable for high-speed generation tasks.
Stefano Goria, Levent A. Mengütürk, Murat C. Mengütürk, Berkan Sesen
arXiv:2512.14190 · cs.LG, math.PR · submitted Dec 16, 2025 · updated Apr 4, 2026
abstract · pdf · html
Competitive FID scores with significantly fewer sampling steps compared to standard diffusion models The framework is flexible — it generalises several existing approaches including score-based diffusion and flow matching Reduced computational cost at inference time while maintaining sample quality
We developed this at A.I.M. Research Lab with co-authors from UCL and the Bank of England. The motivation came from practical experience with generative models in production settings where inference cost matters. Paper: https://arxiv.org/abs/2512.14190 Happy to answer questions about the theory or practical implications.