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.

Despite recent advances in subquadratic attention mechanisms or state-space models, processing long token sequences still imposes significant computational requirements. Token merging has emerged as a solution to increase computational efficiency in computer vision architectures. In this work, we perform the first investigations of token merging in time series analysis on both transformers and state-space models. We further introduce local merging, a domain-specific token merging algorithm that selectively combines tokens within a local neighborhood, achieving two major benefits: a) Local merging can adjust its computational complexity from quadratic to linear based on the neighborhood size to effectively scale to long sequences; b) Local merging is the first causal merging scheme enabling token merging in transformer decoders. Further, we identify spectral properties of the input data that reliably predict the potential benefits of local merging without requiring evaluation on downstream tasks. Our comprehensive empirical evaluation demonstrates that local merging offers substantial efficiency gains with minimal impact on accuracy, achieving up to 5400% acceleration on the recently proposed Chronos foundation model.

In this work, we introduce TreeGen, a novel generative framework modeling distributions over hierarchies. We extend Bayesian Flow Networks (BFNs) to enable transitions between probabilistic and discrete hierarchies parametrized via categorical distributions. Our proposed scheduler provides smooth and consistent entropy decay across varying numbers of categories. We empirically evaluate TreeGen on the jet-clustering task in high-energy physics, demonstrating that it consistently generates valid trees that adhere to physical constraints and closely align with ground-truth log-likelihoods. Finally, by comparing TreeGen’s samples to the exact posterior distribution and performing likelihood maximization via rejection sampling, we demonstrate that TreeGen outperforms various baselines.

Hierarchical clustering has usually been addressed by discrete optimization using heuristics or continuous optimization of relaxed scores for hierarchies. In this work, we propose to optimize expected scores under a probabilistic model over hierarchies. (1) We show theoretically that the global optimal values of the expected Dasgupta cost and Tree-Sampling divergence (TSD), two unsupervised metrics for hierarchical clustering, are equal to the optimal values of their discrete counterparts contrary to some relaxed scores. (2) We propose Expected Probabilistic Hierarchies (EPH), a probabilistic model to learn hierarchies in data by optimizing expected scores. EPH uses differentiable hierarchy sampling enabling end-to-end gradient descent based optimization, and an unbiased subgraph sampling approach to scale to large datasets. (3) We evaluate EPH on synthetic and real-world datasets including vector and graph datasets. EPH outperforms all other approaches quantitatively and provides meaningful hierarchies in qualitative evaluations.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally-trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (*predict*). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (*refine*). Notably, the generative performance of the model remains intact — downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (*synthesize*). Our code is available at https://github.com/amazon-science/unconditional-time-series-diffusion

Modeling of brain tumor dynamics has the potential to advance therapeutic planning. Current modeling approaches resort to numerical solvers that simulate the tumor progression according to a given differential equation. Using highly-efficient numerical solvers, a single forward simulation takes up to a few minutes of compute. At the same time, clinical applications of tumor modeling often imply solving an inverse problem, requiring up to tens of thousands of forward model evaluations when used for a Bayesian model personalization via sampling. This results in a total inference time prohibitively expensive for clinical translation. While recent data-driven approaches become capable of emulating physics simulation, they tend to fail in generalizing over the variability of the boundary conditions imposed by the patient-specific anatomy. In this paper, we propose a learnable surrogate for simulating tumor growth which maps the biophysical model parameters directly to simulation outputs, i.e. the local tumor cell densities, whilst respecting patient geometry. We test the neural solver in a Bayesian model personalization task for a cohort of glioma patients. Bayesian inference using the proposed surrogate yields estimates analogous to those obtained by solving the forward model with a regular numerical solver. The near real-time computation cost renders the proposed method suitable for clinical settings. The code is available at https://github.com/IvanEz/tumor-surrogate.