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In light of the widespread success of generative models, a significant amount of research has gone into speeding up their sampling time. However, generative models are often sampled multiple times to obtain a diverse set incurring a cost…
Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. The worst-case hardness of SAT lies at the core of computational complexity theory. The average-case analysis of SAT has triggered the…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed {\em deterministic} optimization problems. These methods employ constant step-sizes and converge…
Generative diffusion models, famous for their performance in image generation, are popular in various cross-domain applications. However, their use in the communication community has been mostly limited to auxiliary tasks like data modeling…
While the mathematical foundations of score-based generative models are increasingly well understood for unconstrained Euclidean spaces, many practical applications involve data restricted to bounded domains. This paper provides a…
Discrete flow models offer a powerful framework for learning distributions over discrete state spaces and have demonstrated superior performance compared to the discrete diffusion models. However, their convergence properties and error…
Creation of a synthetic dataset that faithfully represents the data distribution and simultaneously preserves privacy is a major research challenge. Many space partitioning based approaches have emerged in recent years for answering…
This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…
Score-based models generate samples by mapping noise to data (and vice versa) via a high-dimensional diffusion process. We question whether it is necessary to run this entire process at high dimensionality and incur all the inconveniences…
The basic random $k$-SAT problem is: Given a set of $n$ Boolean variables, and $m$ clauses of size $k$ picked uniformly at random from the set of all such clauses on our variables, is the conjunction of these clauses satisfiable? Here we…
Variational autoencoders have been widely applied for natural language generation, however, there are two long-standing problems: information under-representation and posterior collapse. The former arises from the fact that only the last…
Building on the remarkable achievements in generative sampling of natural images, we propose an innovative challenge, potentially overly ambitious, which involves generating samples of entire multivariate time series that resemble images.…
Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…
The success of denoising diffusion models raises important questions regarding their generalisation behaviour, particularly in high-dimensional settings. Notably, it has been shown that when training and sampling are performed perfectly,…
We present a novel approach for generating minority samples that live on low-density regions of a data manifold. Our framework is built upon diffusion models, leveraging the principle of guided sampling that incorporates an arbitrary…
Diffusion models are one of the key architectures of generative AI. Their main drawback, however, is the computational costs. This study indicates that the concept of sparsity, well known especially in statistics, can provide a pathway to…
Despite the progress in the development of generative models, their usefulness in creating synthetic data that improve prediction performance of classifiers has been put into question. Besides heuristic principles such as "synthetic data…
An instance of a random constraint satisfaction problem defines a random subset S (the set of solutions) of a large product space (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and…
Dataset distillation reduces the storage and computational consumption of training a network by generating a small surrogate dataset that encapsulates rich information of the original large-scale one. However, previous distillation methods…