We derive a novel generative model from the simple act of Gaussian posterior inference. Treating the generated sample as an unknown variable to infer lets us formulate the sampling process in the language of Bayesian probability. Our model uses a sequence of prediction and posterior update steps to narrow down the unknown sample from a broad initial belief. In addition to a rigorous theoretical analysis, we establish a connection between our model and diffusion models and show that it includes Bayesian Flow Networks (BFNs) as a special case. In our experiments, we demonstrate improved performance over both BFNs and Variational Diffusion Models, achieving competitive likelihood scores on CIFAR10 and ImageNet.

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 enables efficient, parallel sampling and flexible generation for complex conditional tasks defined on the metric space. 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 than autoregressive baselines.

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 that simplifies the generative problem by 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 in forecasting benchmarks, surpassing other methods on 6 out of 8 datasets. However, these models typically transform non-i.i.d. This can hinder the generative process and potentially limit the models' performance.

Transformer architectures have shown promising results in time series processing. However, despite recent advances in subquadratic attention mechanisms or state-space models, processing very long sequences still imposes significant computational requirements. Token merging, which involves replacing multiple tokens with a single one calculated as their linear combination, has shown to considerably improve the throughput of vision transformer architectures while maintaining accuracy. In this work, we go beyond computer vision and perform the first investigations of token merging in time series analysis on both time series transformers and state-space models. To effectively scale token merging to long sequences, we introduce local merging, a domain-specific token merging algorithm that selectively combines tokens within a local neighborhood, adjusting the computational complexity from linear to quadratic based on the neighborhood size. Our comprehensive empirical evaluation demonstrates that token merging offers substantial computational benefits with minimal impact on accuracy across various models and datasets. On the recently proposed Chronos foundation model, we achieve accelerations up to 5400 % with only minor accuracy degradations.

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).

Most adversarial attacks and defenses focus on perturbations within small $\ell_p$-norm constraints. However, $\ell_p$ threat models cannot capture all relevant semantic-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 adversarial examples beyond $\ell_p$-norm constraints, so-called unrestricted adversarial examples, overcoming their limitations. Unlike traditional methods, ScoreAG maintains the core semantics of images while generating realistic 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 matches the performance 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.