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Single-cell RNA sequencing (scRNA-seq) provides high-dimensional profiles of cellular states, enabling data-driven modeling of cellular dynamics over time. In practice, time-resolved scRNA-seq is collected at only a few discrete time points…

Inverse problems, which involve estimating parameters from incomplete or noisy observations, arise in various fields such as medical imaging, geophysics, and signal processing. These problems are often ill-posed, requiring regularization…

Uncertainty quantification has been a core of the statistical machine learning, but its computational bottleneck has been a serious challenge for both Bayesians and frequentists. We propose a model-based framework in quantifying…

Generative models that can model and predict sequences of future events can, in principle, learn to capture complex real-world phenomena, such as physical interactions. However, a central challenge in video prediction is that the future is…

Understanding temporal dynamics in medical imaging is crucial for applications such as disease progression modeling, treatment planning and anatomical development tracking. However, most deep learning methods either consider only single…

Graph generation aims to sample discrete node and edge attributes while satisfying coupled structural constraints. Diffusion models for graphs often adopt largely factorized forward-noising, and many flow-matching methods start from…

Recent efforts have extended the flow-matching framework to discrete generative modeling. One strand of models directly works with the continuous probabilities instead of discrete tokens, which we colloquially refer to as Continuous-State…

Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…

Recent advancement in generative models have demonstrated remarkable performance across various data modalities. Beyond their typical use in data synthesis, these models play a crucial role in distribution matching tasks such as latent…

Denoising diffusion probabilistic models have transformed image generation with their impressive fidelity and diversity. We show that they also excel in estimating optical flow and monocular depth, surprisingly, without task-specific…

We introduce a novel framework for AI-generated image detection through epistemic uncertainty, aiming to address critical security concerns in the era of generative models. Our key insight stems from the observation that distributional…

Causal inconsistency arises when the underlying causal graphs captured by generative models like \textit{Normalizing Flows} (NFs) are inconsistent with those specified in causal models like \textit{Struct Causal Models} (SCMs). This…

We extend flow matching to ensembles of linear systems in both deterministic and stochastic settings. Averaging over system parameters induces memory leading to a non-Markovian interpolation problem for the stochastic case. In this setting,…

Generative models have gained popularity for their potential applications in imaging science, such as image reconstruction, posterior sampling and data sharing. Flow-based generative models are particularly attractive due to their ability…

Equivocal 3D lesion segmentation exhibits high inter-observer variability. Conventional deterministic models ignore this aleatoric uncertainty, producing over-confident masks that obscure clinical risks. Conversely, while generative methods…

We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…

Score-based generative models are a popular class of generative modelling techniques relying on stochastic differential equations (SDE). From their inception, it was realized that it was also possible to perform generation using ordinary…

Mathematical models are vital interpretive and predictive tools used to assist in the understanding of cell migration. There are typically two approaches to modelling cell migration: either micro-scale, discrete or macro-scale, continuum.…

Computational imaging is crucial in many disciplines from autonomous driving to life sciences. However, traditional model-driven and iterative methods consume large computational power and lack scalability for imaging. Deep learning (DL) is…

We propose SymDiff, a method for constructing equivariant diffusion models using the framework of stochastic symmetrisation. SymDiff resembles a learned data augmentation that is deployed at sampling time, and is lightweight,…