arXiv subjects

Marten Lienen

Publications and source records attributed to Marten Lienen.

12 recordsLinked to original sources

arXiv2026

Generative Modeling with Bayesian Sample Inference

We present a novel view of diffusion-like generative modeling from the perspective of iterative Gaussian posterior inference. By treating the generated sample as an unknown variable, we formulate the sampling process in the language of Bayesian probability: at each step, a model predicts the unknown sample from our current belief state and we compute a posterior belief from that prediction. Based on this formulation, we propose the generative model Bayesian Sample Inference (BSI). In addition to a rigorous theoretical analysis, we show that our perspective includes Bayesian Flow Networks (BFNs) and that BSI and BFNs represent the two opposite ends of a range of isotropic hyper-priors over the initial belief state. In our experiments, we demonstrate that BSI improves sample quality over both BFNs and the closely related Variational Diffusion Models on ImageNet32 and ImageNet64, while achieving equivalent log-likelihoods on both datasets.

cs.LG↗

arXiv2026

Discrete Bayesian Sample Inference for Graph Generation

Generating graph-structured data is crucial in applications such as molecular generation, knowledge graphs, and network analysis. However, their discrete, unordered nature makes them difficult for traditional generative models, leading to the rise of discrete diffusion and flow matching models. In this work, we introduce GraphBSI, a novel one-shot graph generative model based on Bayesian Sample Inference (BSI). Instead of evolving samples directly, GraphBSI iteratively refines a belief over graphs in the continuous space of distribution parameters, naturally handling discrete structures. Further, we state BSI as a stochastic differential equation (SDE) and derive a noise-controlled family of SDEs that preserves the marginal distributions via an approximation of the score function. Our theoretical analysis further reveals the connection to Bayesian Flow Networks and Diffusion models. Finally, in our empirical evaluation, we demonstrate state-of-the-art performance on molecular and synthetic graph generation, outperforming existing one-shot graph generative models on the standard benchmarks Moses and GuacaMol.

cs.LG↗

arXiv2026

Edit-Based Flow Matching for Temporal Point Processes

Temporal point processes (TPPs) are a fundamental tool for modeling event sequences in continuous time, but most existing approaches rely on autoregressive parameterizations that are limited by their sequential sampling. Recent non-autoregressive, diffusion-style models mitigate these issues by jointly interpolating between noise and data through event insertions and deletions in a discrete Markov chain. In this work, we generalize this perspective and introduce an Edit Flow process for TPPs that transports noise to data via insert, delete, and substitute edit operations. By learning the instantaneous edit rates within a continuous-time Markov chain framework, we attain a flexible and efficient model that effectively reduces the total number of necessary edit operations during generation. Empirical results demonstrate the generative flexibility of our unconditionally trained model in a wide range of unconditional and conditional generation tasks on benchmark TPPs.

cs.LG↗

arXiv2025

UnHiPPO: Uncertainty-aware Initialization for State Space Models

State space models are emerging as a dominant model class for sequence problems with many relying on the HiPPO framework to initialize their dynamics. However, HiPPO fundamentally assumes data to be noise-free; an assumption often violated in practice. We extend the HiPPO theory with measurement noise and derive an uncertainty-aware initialization for state space model dynamics. In our analysis, we interpret HiPPO as a linear stochastic control problem where the data enters as a noise-free control signal. We then reformulate the problem so that the data become noisy outputs of a latent system and arrive at an alternative dynamics initialization that infers the posterior of this latent system from the data without increasing runtime. Our experiments show that our initialization improves the resistance of state-space models to noise both at training and inference time. Find our implementation at https://cs.cit.tum.de/daml/unhippo.

cs.LG↗

arXiv2025

Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting

Recent advancements in generative modeling, particularly diffusion models, have opened new directions for time series modeling, achieving state-of-the-art performance in forecasting and synthesis. However, the reliance of diffusion-based models on a simple, fixed prior complicates the generative process since the data and prior distributions differ significantly. We introduce TSFlow, a conditional flow matching (CFM) model for time series combining Gaussian processes, optimal transport paths, and data-dependent prior distributions. By incorporating (conditional) Gaussian processes, TSFlow aligns the prior distribution more closely with the temporal structure of the data, enhancing both unconditional and conditional generation. Furthermore, we propose conditional prior sampling to enable probabilistic forecasting with an unconditionally trained model. In our experimental evaluation on eight real-world datasets, we demonstrate the generative capabilities of TSFlow, producing high-quality unconditional samples. Finally, we show that both conditionally and unconditionally trained models achieve competitive results across multiple forecasting benchmarks.

cs.LG↗

arXiv2025

Assessing Robustness via Score-Based Adversarial Image Generation

Most adversarial attacks and defenses focus on perturbations within small $\ell_p$-norm constraints. However, $\ell_p$ threat models cannot capture all relevant semantics-preserving perturbations, and hence, the scope of robustness evaluations is limited. In this work, we introduce Score-Based Adversarial Generation (ScoreAG), a novel framework that leverages the advancements in score-based generative models to generate unrestricted adversarial examples that overcome the limitations of $\ell_p$-norm constraints. Unlike traditional methods, ScoreAG maintains the core semantics of images while generating adversarial examples, either by transforming existing images or synthesizing new ones entirely from scratch. We further exploit the generative capability of ScoreAG to purify images, empirically enhancing the robustness of classifiers. Our extensive empirical evaluation demonstrates that ScoreAG improves upon the majority of state-of-the-art attacks and defenses across multiple benchmarks. This work highlights the importance of investigating adversarial examples bounded by semantics rather than $\ell_p$-norm constraints. ScoreAG represents an important step towards more encompassing robustness assessments.

cs.CV↗

arXiv2024

Unfolding Time: Generative Modeling for Turbulent Flows in 4D

A recent study in turbulent flow simulation demonstrated the potential of generative diffusion models for fast 3D surrogate modeling. This approach eliminates the need for specifying initial states or performing lengthy simulations, significantly accelerating the process. While adept at sampling individual frames from the learned manifold of turbulent flow states, the previous model lacks the capability to generate sequences, hindering analysis of dynamic phenomena. This work addresses this limitation by introducing a 4D generative diffusion model and a physics-informed guidance technique that enables the generation of realistic sequences of flow states. Our findings indicate that the proposed method can successfully sample entire subsequences from the turbulent manifold, even though generalizing from individual frames to sequences remains a challenging task. This advancement opens doors for the application of generative modeling in analyzing the temporal evolution of turbulent flows, providing valuable insights into their complex dynamics.

physics.flu-dyn↗

arXiv2024

From Zero to Turbulence: Generative Modeling for 3D Flow Simulation

Simulations of turbulent flows in 3D are one of the most expensive simulations in computational fluid dynamics (CFD). Many works have been written on surrogate models to replace numerical solvers for fluid flows with faster, learned, autoregressive models. However, the intricacies of turbulence in three dimensions necessitate training these models with very small time steps, while generating realistic flow states requires either long roll-outs with many steps and significant error accumulation or starting from a known, realistic flow state - something we aimed to avoid in the first place. Instead, we propose to approach turbulent flow simulation as a generative task directly learning the manifold of all possible turbulent flow states without relying on any initial flow state. For our experiments, we introduce a challenging 3D turbulence dataset of high-resolution flows and detailed vortex structures caused by various objects and derive two novel sample evaluation metrics for turbulent flows. On this dataset, we show that our generative model captures the distribution of turbulent flows caused by unseen objects and generates high-quality, realistic samples amenable for downstream applications without access to any initial state.

physics.flu-dyn↗

arXiv2024

Add and Thin: Diffusion for Temporal Point Processes

Autoregressive neural networks within the temporal point process (TPP) framework have become the standard for modeling continuous-time event data. Even though these models can expressively capture event sequences in a one-step-ahead fashion, they are inherently limited for long-term forecasting applications due to the accumulation of errors caused by their sequential nature. To overcome these limitations, we derive ADD-THIN, a principled probabilistic denoising diffusion model for TPPs that operates on entire event sequences. Unlike existing diffusion approaches, ADD-THIN naturally handles data with discrete and continuous components. In experiments on synthetic and real-world datasets, our model matches the state-of-the-art TPP models in density estimation and strongly outperforms them in forecasting.

cs.LG↗

arXiv2023

torchode: A Parallel ODE Solver for PyTorch

We introduce an ODE solver for the PyTorch ecosystem that can solve multiple ODEs in parallel independently from each other while achieving significant performance gains. Our implementation tracks each ODE's progress separately and is carefully optimized for GPUs and compatibility with PyTorch's JIT compiler. Its design lets researchers easily augment any aspect of the solver and collect and analyze internal solver statistics. In our experiments, our implementation is up to 4.3 times faster per step than other ODE solvers and it is robust against within-batch interactions that lead other solvers to take up to 4 times as many steps. Code available at https://github.com/martenlienen/torchode

cs.LG↗

arXiv2022

Scalable Optimal Transport in High Dimensions for Graph Distances, Embedding Alignment, and More

The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for large sets of objects. In this work we propose two effective log-linear time approximations of the cost matrix: First, a sparse approximation based on locality-sensitive hashing (LSH) and, second, a Nyström approximation with LSH-based sparse corrections, which we call locally corrected Nyström (LCN). These approximations enable general log-linear time algorithms for entropy-regularized OT that perform well even for the complex, high-dimensional spaces common in deep learning. We analyse these approximations theoretically and evaluate them experimentally both directly and end-to-end as a component for real-world applications. Using our approximations for unsupervised word embedding alignment enables us to speed up a state-of-the-art method by a factor of 3 while also improving the accuracy by 3.1 percentage points without any additional model changes. For graph distance regression we propose the graph transport network (GTN), which combines graph neural networks (GNNs) with enhanced Sinkhorn. GTN outcompetes previous models by 48% and still scales log-linearly in the number of nodes.

cs.LG↗

arXiv2022

Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networks

We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data via the finite element method. The resulting graph neural network estimates the instantaneous effects of the unknown dynamics on each cell in a meshing of the spatial domain. Our model can incorporate prior knowledge via assumptions on the form of the unknown PDE, which induce a structural bias towards learning specific processes. Through this mechanism, we derive a transport variant of our model from the convection equation and show that it improves the transfer performance to higher-resolution meshes on sea surface temperature and gas flow forecasting against baseline models representing a selection of spatio-temporal forecasting methods. A qualitative analysis shows that our model disentangles the data dynamics into their constituent parts, which makes it uniquely interpretable.

cs.LG↗