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Gabriel Nobis

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4 papers

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NeurIPS Conference 2025 Conference Paper

Fractional Diffusion Bridge Models

Gabriel Nobis
Maximilian Springenberg
Arina Belova
Rembert Daems
Christoph Knochenhauer
Manfred Opper
Tolga Birdal
Wojciech Samek

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$_\alpha$ atomic positions in protein structure prediction and lower Fréchet Inception Distance (FID) in unpaired image translation.

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NeurIPS Conference 2024 Conference Paper

Generative Fractional Diffusion Models

Gabriel Nobis
Maximilian Springenberg
Marco Aversa
Michael Detzel
Rembert Daems
Roderick Murray-Smith
Shinichi Nakajima
Sebastian Lapuschkin

We introduce the first continuous-time score-based generative model that leverages fractional diffusion processes for its underlying dynamics. Although diffusion models have excelled at capturing data distributions, they still suffer from various limitations such as slow convergence, mode-collapse on imbalanced data, and lack of diversity. These issues are partially linked to the use of light-tailed Brownian motion (BM) with independent increments. In this paper, we replace BM with an approximation of its non-Markovian counterpart, fractional Brownian motion (fBM), characterized by correlated increments and Hurst index $H \in (0, 1)$, where $H=0. 5$ recovers the classical BM. To ensure tractable inference and learning, we employ a recently popularized Markov approximation of fBM (MA-fBM) and derive its reverse-time model, resulting in *generative fractional diffusion models* (GFDM). We characterize the forward dynamics using a continuous reparameterization trick and propose *augmented score matching* to efficiently learn the score function, which is partly known in closed form, at minimal added cost. The ability to drive our diffusion model via MA-fBM offers flexibility and control. $H \leq 0. 5$ enters the regime of *rough paths* whereas $H>0. 5$ regularizes diffusion paths and invokes long-term memory. The Markov approximation allows added control by varying the number of Markov processes linearly combined to approximate fBM. Our evaluations on real image datasets demonstrate that GFDM achieves greater pixel-wise diversity and enhanced image quality, as indicated by a lower FID, offering a promising alternative to traditional diffusion models

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TMLR Journal 2023 Journal Article

Data Models for Dataset Drift Controls in Machine Learning With Optical Images

Luis Oala
Marco Aversa
Gabriel Nobis
Kurt Willis
Yoan Neuenschwander
Michèle Buck
Christian Matek
Jerome Extermann

Camera images are ubiquitous in machine learning research. They also play a central role in the delivery of important public services spanning medicine or environmental surveying. However, the application of machine learning models in these domains has been limited because of robustness concerns. A primary failure mode are performance drops due to differences between the training and deployment data. While there are methods to prospectively validate the robustness of machine learning models to such dataset drifts, existing approaches do not account for explicit models of machine learning's primary object of interest: the data. This limits our ability to study and understand the relationship between data generation and downstream machine learning model performance in a physically accurate manner. In this study, we demonstrate how to overcome this limitation by pairing traditional machine learning with physical optics to obtain explicit and differentiable data models. We demonstrate how such data models can be constructed for image data and used to control downstream machine learning model performance related to dataset drift. The findings are distilled into three applications. First, drift synthesis enables the controlled generation of physically faithful drift test cases to power model selection and targeted generalization. Second, the gradient connection between machine learning task model and data model allows advanced, precise tolerancing of task model sensitivity to changes in the data generation. These drift forensics can be used to precisely specify the acceptable data environments in which a task model may be run. Third, drift optimization opens up the possibility to create drifts that can help the task model learn better faster, effectively optimizing the data generating process itself to support the downstream machine vision task. This is an interesting upgrade to existing imaging pipelines which traditionally have been optimized to be consumed by human users but not machine learning models. Alongside the data model code we release two datasets to the public that we collected as part of this work. In total, the two datasets, Raw-Microscopy and Raw-Drone, comprise 1,488 scientifically calibrated reference raw sensor measurements, 8,928 raw intensity variations as well as 17,856 images processed through twelve data models with different configurations. A guide to access the open code and datasets is available at https://github.com/aiaudit-org/raw2logit.

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NeurIPS Conference 2023 Conference Paper

DiffInfinite: Large Mask-Image Synthesis via Parallel Random Patch Diffusion in Histopathology

Marco Aversa
Gabriel Nobis
Miriam Hägele
Kai Standvoss
Mihaela Chirica
Roderick Murray-Smith
Ahmed M. Alaa
Lukas Ruff

We present DiffInfinite, a hierarchical diffusion model that generates arbitrarily large histological images while preserving long-range correlation structural information. Our approach first generates synthetic segmentation masks, subsequently used as conditions for the high-fidelity generative diffusion process. The proposed sampling method can be scaled up to any desired image size while only requiring small patches for fast training. Moreover, it can be parallelized more efficiently than previous large-content generation methods while avoiding tiling artifacts. The training leverages classifier-free guidance to augment a small, sparsely annotated dataset with unlabelled data. Our method alleviates unique challenges in histopathological imaging practice: large-scale information, costly manual annotation, and protective data handling. The biological plausibility of DiffInfinite data is evaluated in a survey by ten experienced pathologists as well as a downstream classification and segmentation task. Samples from the model score strongly on anti-copying metrics which is relevant for the protection of patient data.

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