Publications

2026

1. Preprint

   INDEQS: Informed Neural controlled Differential EQuationS

   Michael Detzel, Gabriel Nobis, Kristiyan Blagov, Juri Schubert, Jackie Ma, and Wojciech Samek

   2026

   Abs arXiv Bib PDF Code

   Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where a directed graph structure is known a priori. We introduce Informed Neural controlled Differential EQuationS (INDEQS), a graph-based NCDE forecasting method that incorporates prior knowledge of a directed graph at distinct architectural positions. INDEQS separates inner mixing of hidden states across graph nodes from outer mixing between vector field and control, and offers both a lightweight graph-constrained variant and a more expressive variant, learning additional graph connections from data via adaptive graph convolutions. To systematically study when graph informedness is beneficial in forecasting, we devise a continuous advection simulation on directed graphs, yielding synthetic spatio-temporal datasets with known ground-truth flow structure. We then evaluate INDEQS on two real-world tasks: river discharge forecasting on a hydrological network and traffic flow prediction on PeMS08. Across these synthetic and real-world benchmarks, outer informedness consistently improves mean absolute error over an uninformed NCDE with comparable parameter count, particularly on larger graphs, while inner informedness offers a more parameter-efficient alternative when strict adherence to a known adjacency is desired. A comparison of discrete convolutional and continuous-time decoders further shows that continuous decoders yield better accuracy and greater temporal flexibility on real-world tasks. An implementation of INDEQS and the advection simulation is available at github.com/Mitchi1/indeqs.

   @misc{detzel2026indeqsinformedneuralcontrolled,
     title = {INDEQS: Informed Neural controlled Differential EQuationS},
     author = {Detzel, Michael and Nobis, Gabriel and Blagov, Kristiyan and Schubert, Juri and Ma, Jackie and Samek, Wojciech},
     year = {2026},
     eprint = {2606.19138},
     archiveprefix = {arXiv},
     primaryclass = {cs.LG},
     url = {https://arxiv.org/abs/2606.19138},
   }

2025

1. NeurIPS

   Fractional Diffusion Bridge Models

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

   In Advances in Neural Information Processing Systems , 2025

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   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_αatomic positions in protein structure prediction and lower Fréchet Inception Distance (FID) in unpaired image translation.

   @inproceedings{nobis2025fractional,
     title = {Fractional Diffusion Bridge Models},
     author = {Nobis, Gabriel and Springenberg, Maximilian and Belova, Arina and Daems, Rembert and Knochenhauer, Christoph and Opper, Manfred and Birdal, Tolga and Samek, Wojciech},
     booktitle = {Advances in Neural Information Processing Systems},
     year = {2025},
     url = {https://arxiv.org/abs/2511.01795},
   }

2024

1. NeurIPS

   Generative Fractional Diffusion Models

   Gabriel Nobis, Maximilian Springenberg, Marco Aversa, Michael Detzel, Rembert Daems, Roderick Murray-Smith, Shinichi Nakajima, Sebastian Lapuschkin, Stefano Ermon, Tolga Birdal, Manfred Opper, Christoph Knochenhauer, Luis Oala, and Wojciech Samek

   In Advances in Neural Information Processing Systems , 2024

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   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 ∈(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 ≤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.

   @inproceedings{nobis2024generative,
     title = {Generative Fractional Diffusion Models},
     author = {Nobis, Gabriel and Springenberg, Maximilian and Aversa, Marco and Detzel, Michael and Daems, Rembert and Murray-Smith, Roderick and Nakajima, Shinichi and Lapuschkin, Sebastian and Ermon, Stefano and Birdal, Tolga and Opper, Manfred and Knochenhauer, Christoph and Oala, Luis and Samek, Wojciech},
     booktitle = {Advances in Neural Information Processing Systems},
     pages = {25469--25509},
     volume = {37},
     year = {2024},
   }

2. NeurIPS Workshop

   Spatial Shortcuts in Graph Neural Controlled Differential Equations

   Michael Detzel, Gabriel Nobis, Jackie Ma, and Wojciech Samek

   In NeurIPS 2024 Workshop on Data-driven and Differentiable Simulations, Surrogates, and Solvers , 2024

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   We incorporate prior graph topology information into a Neural Controlled Differential Equation (NCDE) to predict the future states of a dynamical system defined on a graph. The informed NCDE infers the future dynamics at the vertices of simulated advection data on graph edges with a known causal graph, observed only at vertices during training. We investigate different positions in the model architecture to inform the NCDE with graph information and identify an outer position between hidden state and control as theoretically and empirically favorable. Our such informed NCDE requires fewer parameters to reach a lower Mean Absolute Error (MAE) compared to previous methods that do not incorporate additional graph topology information.

   @inproceedings{detzel2024spatial,
     title = {Spatial Shortcuts in Graph Neural Controlled Differential Equations},
     author = {Detzel, Michael and Nobis, Gabriel and Ma, Jackie and Samek, Wojciech},
     booktitle = {NeurIPS 2024 Workshop on Data-driven and Differentiable Simulations, Surrogates, and Solvers},
     year = {2024},
     url = {https://openreview.net/forum?id=tfVjODycMk},
   }

2023

1. NeurIPS

   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, Daniela Ivanova, Wojciech Samek, Frederick Klauschen, Bruno Sanguinetti, and Luis Oala

   In Advances in Neural Information Processing Systems , 2023

   Abs Bib PDF Code Website

   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.

   @inproceedings{aversa2023diffinfinite,
     author = {Aversa, Marco and Nobis, Gabriel and H\"{a}gele, Miriam and Standvoss, Kai and Chirica, Mihaela and Murray-Smith, Roderick and Alaa, Ahmed M. and Ruff, Lukas and Ivanova, Daniela and Samek, Wojciech and Klauschen, Frederick and Sanguinetti, Bruno and Oala, Luis},
     booktitle = {Advances in Neural Information Processing Systems},
     pages = {78126--78141},
     title = {DiffInfinite: Large Mask-Image Synthesis via Parallel Random Patch Diffusion in Histopathology},
     url = {https://proceedings.neurips.cc/paper_files/paper/2023/file/f64927f5de00c47899e6e58c731966b6-Paper-Datasets_and_Benchmarks.pdf},
     volume = {36},
     year = {2023},
   }

2. TMLR

   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, Enrico Pomarico, Wojciech Samek, Roderick Murray-Smith, Christoph Clausen, and Bruno Sanguinetti

   Transactions on Machine Learning Research, 2023

   Abs

   Camera images are ubiquitous in machine learning research. They also play a central role in the delivery of important services spanning medicine and 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 the primary object of interest: the data. This makes it difficult to create physically faithful drift test cases or to provide precise specifications of data models that should be avoided during the deployment of a machine learning model. In this study, we demonstrate how these shortcomings can be overcome by pairing machine learning robustness validation with physical optics. We examine the role raw sensor data and differentiable data models can play in controlling performance risks related to image dataset drift. The findings are distilled into three applications. First, drift synthesis enables the controlled generation of physically faithful drift test cases. The results for absolute and relative changes in task model performance obtained with our method diverge markedly from an augmentation testing alternative that is not physically faithful. Second, the gradient connection between machine learning model and our data models allows for drift forensics that can be used to specify performance-sensitive data models which should be avoided during deployment of a machine learning model. Third, drift adjustment opens up the possibility for processing adjustments in the face of drift. This can lead to speed up and stabilization of classifier training at a margin of up to 20% in validation accuracy. Alongside our 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 our data models with twelve different configurations. A guide to access the open code and datasets is available at github.com/aiaudit-org/raw2logit.

2020

1. NeurIPS Workshop

   ML4H Auditing: From Paper to Practice

   Luis Oala, Jana Fehr, Luca Gilli, Pradeep Balachandran, Alixandro Werneck Leite, Saul Calderon-Ramirez, Danny Xie Li, Gabriel Nobis, Erick Alejandro Muñoz Alvarado, Giovanna Jaramillo-Gutierrez, Christian Matek, Arun Shroff, Ferath Kherif, Bruno Sanguinetti, and Thomas Wiegand

   In Proceedings of the Machine Learning for Health NeurIPS Workshop , 11 dec 2020

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   Healthcare systems are currently adapting to digital technologies, producing large quantities of novel data. Based on these data, machine-learning algorithms have been developed to support practitioners in labor-intensive workflows such as diagnosis, prognosis, triage or treatment of disease. However, their translation into medical practice is often hampered by a lack of careful evaluation in different settings. Efforts have started worldwide to establish guidelines for evaluating machine learning for health (ML4H) tools, highlighting the necessity to evaluate models for bias, interpretability, robustness, and possible failure modes. However, testing and adopting these guidelines in practice remains an open challenge. In this work, we target the paper-to-practice gap by applying an ML4H audit framework proposed by the ITU/WHO Focus Group on Artificial Intelligence for Health (FG-AI4H) to three use cases: diagnostic prediction of diabetic retinopathy, diagnostic prediction of Alzheimer’s disease, and cytomorphologic classification for leukemia diagnostics. The assessment comprises dimensions such as bias, interpretability, and robustness. Our results highlight the importance of fine-grained and caseadapted quality assessment, provide support for incorporating proposed quality assessment considerations of ML4H during the entire development life cycle, and suggest improvements for future ML4H reference evaluation frameworks.