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Diffusion models have achieved great success in modeling continuous data modalities such as images, audio, and video, but have seen limited use in discrete domains such as language. Recent attempts to adapt diffusion to language have…

Blind deconvolution problems are severely ill-posed because neither the underlying signal nor the forward operator are not known exactly. Conventionally, these problems are solved by alternating between estimation of the image and kernel…

This survey paper provides a comprehensive review of the use of diffusion models in natural language processing (NLP). Diffusion models are a class of mathematical models that aim to capture the diffusion of information or signals across a…

Clustering algorithms partition a dataset into groups of similar points. The clustering problem is very general, and different partitions of the same dataset could be considered correct and useful. To fully understand such data, it must be…

Masked (or absorbing) diffusion is actively explored as an alternative to autoregressive models for generative modeling of discrete data. However, existing work in this area has been hindered by unnecessarily complex model formulations and…

With the rise of large-scale foundation models, efficiently adapting them to downstream tasks remains a central challenge. Linear probing, which freezes the backbone and trains a lightweight head, is computationally efficient but often…

For the last decade, there has been a push to use multi-dimensional (latent) spaces to represent concepts; and yet how to manipulate these concepts or reason with them remains largely unclear. Some recent methods exploit multiple latent…

Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology…

High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…

Diffusion models have shown exceptional scaling properties in the image synthesis domain, and initial attempts have shown similar benefits for applying diffusion to unconditional text synthesis. Denoising diffusion models attempt to…

Anomalies are samples that significantly deviate from the rest of the data and their detection plays a major role in building machine learning models that can be reliably used in applications such as data-driven design and novelty…

Recent progress in imitation learning has been enabled by policy architectures that scale to complex visuomotor tasks, multimodal distributions, and large datasets. However, these methods often rely on learning from large amount of expert…

Nowadays many real-world datasets can be considered as functional, in the sense that the processes which generate them are continuous. A fundamental property of this type of data is that in theory they belong to an infinite-dimensional…

In this study, we develop a method for multi-task manifold learning. The method aims to improve the performance of manifold learning for multiple tasks, particularly when each task has a small number of samples. Furthermore, the method also…

Disentangled representation learning strives to extract the intrinsic factors within observed data. Factorizing these representations in an unsupervised manner is notably challenging and usually requires tailored loss functions or specific…

Despite recent advancements in latent diffusion models that generate high-dimensional image data and perform various downstream tasks, there has been little exploration into perceptual consistency within these models on the task of…

Seismic acoustic impedance plays a crucial role in lithological identification and subsurface structure interpretation. However, due to the inherently ill-posed nature of the inversion problem, directly estimating impedance from post-stack…

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

A conditional latent-diffusion based framework for solving the electromagnetic inverse scattering problem associated with microwave imaging is introduced. This generative machine-learning model explicitly mirrors the non-uniqueness of the…

We study the problem of diffusion-based network learning of a nonlinear phenomenon, $m$, from local agents' measurements collected in a noisy environment. For a decentralized network and information spreading merely between directly…