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.

Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning models for point processes are predominantly constrained by their reliance on the characteristic intensity function, introducing an inherent trade-off between efficiency and flexibility. In this paper, we introduce Point Set Diffusion, a diffusion-based latent variable model that can represent arbitrary point processes on general metric spaces without relying on the intensity function. By directly learning to stochastically interpolate between noise and data point sets, our approach effectively captures the distribution of point processes and enables efficient, parallel sampling and flexible generation for complex conditional tasks. Experiments on synthetic and real-world datasets demonstrate that Point Set Diffusion achieves state-of-the-art performance in unconditional and conditional generation of spatial and spatiotemporal point processes while providing up to orders of magnitude faster sampling.

Building generative models for relational databases (RDBs) is important for many applications, such as privacy-preserving data release and augmenting real datasets. However, most prior works either focus on single-table generation or adapt single-table models to the multi-table setting by relying on autoregressive factorizations and sequential generation. These approaches limit parallelism, restrict flexibility in downstream applications, and compound errors due to commonly made conditional independence assumptions. In this paper, we propose a fundamentally different approach: jointly modeling all tables in an RDB without imposing any table order. By using a natural graph representation of RDBs, we propose the Graph-Conditional Relational Diffusion Model (GRDM), which leverages a graph neural network to jointly denoise row attributes and capture complex inter-table dependencies. Extensive experiments on six real-world RDBs demonstrate that our approach substantially outperforms autoregressive baselines in modeling multi-hop inter-table correlations and achieves state-of-the-art performance on single-table fidelity metrics. Our code is available at https://github.com/ketatam/rdb-diffusion.

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.

Statistical shape models are an essential tool for various tasks in medical image analysis, including shape generation, reconstruction and classification. Shape models are learned from a population of example shapes, which are typically obtained through segmentation of volumetric medical images. In clinical practice, highly anisotropic volumetric scans with large slice distances are prevalent, e.g., to reduce radiation exposure in CT or image acquisition time in MR imaging. For existing shape modeling approaches, the resolution of the emerging model is limited to the resolution of the training shapes. Therefore, any missing information between slices prohibits existing methods from learning a high-resolution shape prior. We propose a novel shape modeling approach that can be trained on sparse, binary segmentation masks with large slice distances. This is achieved through employing continuous shape representations based on neural implicit functions. After training, our model can reconstruct shapes from various sparse inputs at high target resolutions beyond the resolution of individual training examples. We successfully reconstruct high-resolution shapes from as few as three orthogonal slices. Furthermore, our shape model allows us to embed various sparse segmentation masks into a common, low-dimensional latent space - independent of the acquisition direction, resolution, spacing, and field of view. We show that the emerging latent representation discriminates between healthy and pathological shapes, even when provided with sparse segmentation masks. Lastly, we qualitatively demonstrate that the emerging latent space is smooth and captures characteristic modes of shape variation. We evaluate our shape model on two anatomical structures: the lumbar vertebra and the distal femur, both from publicly available datasets.

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.