Fractional Diffusion Bridge Models
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911247562178560 |
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| author | Nobis, Gabriel Springenberg, Maximilian Belova, Arina Daems, Rembert Knochenhauer, Christoph Opper, Manfred Birdal, Tolga Samek, Wojciech |
| author_facet | Nobis, Gabriel Springenberg, Maximilian Belova, Arina Daems, Rembert Knochenhauer, Christoph Opper, Manfred Birdal, Tolga Samek, Wojciech |
| contents | We present Fractional Diffusion Bridge Models (FDBM), a novel generative diffusion bridge framework driven by an approximation of the rich and non-Markovian fractional Brownian motion (fBM). Real stochastic processes exhibit a degree of memory effects (correlations in time), long-range dependencies, roughness and anomalous diffusion phenomena that are not captured in standard diffusion or bridge modeling due to the use of Brownian motion (BM). As a remedy, leveraging a recent Markovian approximation of fBM (MA-fBM), we construct FDBM that enable tractable inference while preserving the non-Markovian nature of fBM. We prove the existence of a coupling-preserving generative diffusion bridge and leverage it for future state prediction from paired training data. We then extend our formulation to the Schrödinger bridge problem and derive a principled loss function to learn the unpaired data translation. We evaluate FDBM on both tasks: predicting future protein conformations from aligned data, and unpaired image translation. In both settings, FDBM achieves superior performance compared to the Brownian baselines, yielding lower root mean squared deviation (RMSD) of C$_α$ atomic positions in protein structure prediction and lower Fréchet Inception Distance (FID) in unpaired image translation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01795 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional Diffusion Bridge Models Nobis, Gabriel Springenberg, Maximilian Belova, Arina Daems, Rembert Knochenhauer, Christoph Opper, Manfred Birdal, Tolga Samek, Wojciech Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition Robotics We present Fractional Diffusion Bridge Models (FDBM), a novel generative diffusion bridge framework driven by an approximation of the rich and non-Markovian fractional Brownian motion (fBM). Real stochastic processes exhibit a degree of memory effects (correlations in time), long-range dependencies, roughness and anomalous diffusion phenomena that are not captured in standard diffusion or bridge modeling due to the use of Brownian motion (BM). As a remedy, leveraging a recent Markovian approximation of fBM (MA-fBM), we construct FDBM that enable tractable inference while preserving the non-Markovian nature of fBM. We prove the existence of a coupling-preserving generative diffusion bridge and leverage it for future state prediction from paired training data. We then extend our formulation to the Schrödinger bridge problem and derive a principled loss function to learn the unpaired data translation. We evaluate FDBM on both tasks: predicting future protein conformations from aligned data, and unpaired image translation. In both settings, FDBM achieves superior performance compared to the Brownian baselines, yielding lower root mean squared deviation (RMSD) of C$_α$ atomic positions in protein structure prediction and lower Fréchet Inception Distance (FID) in unpaired image translation. |
| title | Fractional Diffusion Bridge Models |
| topic | Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition Robotics |
| url | https://arxiv.org/abs/2511.01795 |