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Variational Inference is a powerful tool in the Bayesian modeling toolkit, however, its effectiveness is determined by the expressivity of the utilized variational distributions in terms of their ability to match the true posterior…
Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…
In this paper we study supervised learning tasks on the space of probability measures. We approach this problem by embedding the space of probability measures into $L^2$ spaces using the optimal transport framework. In the embedding spaces,…
Increasingly large parameter spaces, used to more accurately model precision observables in physics, can paradoxically lead to large deviations in the inferred parameters of interest -- a bias known as volume projection effects -- when…
Diffusion models are a powerful class of generative models capable of producing high-quality images from pure noise using a simple text prompt. While most methods which introduce additional spatial constraints into the generated images…
Downscaling techniques are one of the most prominent applications of Deep Learning (DL) in Earth System Modeling. A robust DL downscaling model can generate high-resolution fields from coarse-scale numerical model simulations, saving the…
Diffusion Models (DMs) iteratively denoise random samples to produce high-quality data. The iterative sampling process is derived from Stochastic Differential Equations (SDEs), allowing a speed-quality trade-off chosen at inference. Another…
Despite the success of diffusion models, the training and inference of diffusion models are notoriously expensive due to the long chain of the reverse process. In parallel, the Lottery Ticket Hypothesis (LTH) claims that there exists…
Due to its geometric properties, hyperbolic space can support high-fidelity embeddings of tree- and graph-structured data, upon which various hyperbolic networks have been developed. Existing hyperbolic networks encode geometric priors not…
Diffusion models have emerged as powerful generative approaches for missing-data imputation, yet most existing methods operate directly in data space and degrade when training data are heavily incomplete. We investigate whether shifting…
Augmentation for dense prediction typically relies on either sample mixing or generative synthesis. Mixing improves robustness but misaligned masks yield soft label ambiguity. Diffusion synthesis increases apparent diversity but, when…
Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the…
Diffusion models are state-of-the-art tools for various generative tasks. Yet training these models involves estimating high-dimensional score functions, which in principle suffers from the curse of dimensionality. It is therefore important…
In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes…
Established methods for unsupervised representation learning such as variational autoencoders produce none or poorly calibrated uncertainty estimates making it difficult to evaluate if learned representations are stable and reliable. In…
Modern large language models (LLMs) excel at tasks that require storing and retrieving knowledge, such as factual recall and question answering. Transformers are central to this capability because they can encode information during training…
Laplacian pyramid based Laurent polynomial (LP$^2$) matrices are generated by Laurent polynomial column vectors and have long been studied in connection with Laplacian pyramidal algorithms in Signal Processing. In this paper, we investigate…
The use of Variational Autoencoders in different Machine Learning tasks has drastically increased in the last years. They have been developed as denoising, clustering and generative tools, highlighting a large potential in a wide range of…
Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…
Diffusion models have recently gained recognition for generating diverse and high-quality content, especially in image synthesis. These models excel not only in creating fixed-size images but also in producing panoramic images. However,…