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AI-driven design problems, such as DNA/protein sequence design, are commonly tackled from two angles: generative modeling, which efficiently captures the feasible design space (e.g., natural images or biological sequences), and model-based…

Learning a causal directed acyclic graph from data is a challenging task that involves solving a combinatorial problem for which the solution is not always identifiable. A new line of work reformulates this problem as a continuous…

Stochastic gradient methods (SGMs) have been widely used for solving stochastic optimization problems. A majority of existing works assume no constraints or easy-to-project constraints. In this paper, we consider convex stochastic…

Conditional discrete generative models struggle to faithfully compose multiple input conditions. To address this, we derive a theoretically-grounded formulation for composing discrete probabilistic generative processes, with masked…

Conditional discrete generative models struggle to faithfully compose multiple input conditions. To address this, we derive a theoretically-grounded formulation for composing discrete probabilistic generative processes, with masked…

This study develops an algorithm for distributed computing of linear programming problems of huge-scales. Global consensus with single common variable, multiblocks, and augmented Lagrangian are adopted. The consensus is used to partition…

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…

The discovery of inorganic crystal structures with targeted properties is a significant challenge in materials science. Generative models, especially state-of-the-art diffusion models, offer the promise of modeling complex data…

Data-driven generative models excel in language and vision, but diffusion models often fail in constrained planning and design tasks, exhibiting severe constraint violations in engineering inverse design, molecular generation, multi-robot…

We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…

Most recently, He and Yuan [arXiv:2108.08554, 2021] have proposed a balanced augmented Lagrangian method (ALM) for the canonical convex programming problem with linear constraints, which advances the original ALM by balancing its…

Uniform-state discrete diffusion models hold the promise of fast text generation due to their inherent ability to self-correct. However, they are typically outperformed by autoregressive models and masked diffusion models. In this work, we…

In this paper we describe a novel framework for diffusion-based generative modeling on constrained spaces. In particular, we introduce manual bridges, a framework that expands the kinds of constraints that can be practically used to form…

Diffusion models, which iteratively denoise data samples to synthesize high-quality outputs, have achieved empirical success across domains. However, optimizing these models for downstream tasks often involves nested bilevel structures,…

Diffusion-based Handwritten Text Generation (HTG) approaches achieve impressive results on frequent, in-vocabulary words observed at training time and on regular styles. However, they are prone to memorizing training samples and often…

In this work, we design primal and dual bounding methods for multistage adaptive robust optimization (MSARO) problems motivated by two decision rules rooted in the stochastic programming literature. From the primal perspective, this is…

Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding…

In this paper we consider a general, challenging distributed optimization set-up arising in several important network control applications. Agents of a network want to minimize the sum of local cost functions, each one depending on a local…

Diffusion models that are based on iterative denoising have been recently proposed and leveraged in various generation tasks like image generation. Whereas, as a way inherently built for continuous data, existing diffusion models still have…

Recent advances in denoising diffusion models have enabled rapid generation of optimized structures for topology optimization. However, these models often rely on surrogate predictors to enforce physical constraints, which may fail to…