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Discrete state space diffusion models have shown significant advantages in applications involving discrete data, such as text and image generation. It has also been observed that their performance is highly sensitive to the choice of rate…

Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…

Diffusion models are central to modern generative modeling, and understanding how they balance memorization and generalization is critical for reliable deployment. Recent work has shown that memorization in diffusion models is shaped by…

Diffusion models have been successfully adapted to text generation tasks by mapping the discrete text into the continuous space. However, there exist nonnegligible gaps between training and inference, owing to the absence of the forward…

Score-based diffusion models, while achieving minimax optimality for sampling, are often hampered by slow sampling speeds due to the high computational burden of score function evaluations. Despite the recent remarkable empirical advances…

Diffusion models have become a successful approach for solving various image inverse problems by providing a powerful diffusion prior. Many studies tried to combine the measurement into diffusion by score function replacement, matrix…

Significant advances have been made in the sampling efficiency of diffusion models and flow matching models, driven by Consistency Distillation (CD), which trains a student model to mimic the output of a teacher model at a later timestep.…

Diffusion Models~(DMs) have emerged as the dominant approach in Generative Artificial Intelligence (GenAI), owing to their remarkable performance in tasks such as text-to-image synthesis. However, practical DMs, such as stable diffusion,…

Diffusion models have shown strong performance in speech enhancement, but their real-time applicability has been limited by multi-step iterative sampling. Consistency distillation has recently emerged as a promising alternative by…

Generative modeling aims to produce new random examples from an unknown target distribution, given access to a finite collection of examples. Among the leading approaches, denoising diffusion probabilistic models (DDPMs) construct such…

This paper presents a novel theoretical framework for understanding how diffusion models can learn disentangled representations. Within this framework, we establish identifiability conditions for general disentangled latent variable models,…

Discrete diffusion models have emerged as a powerful paradigm for generative modeling on sequence data; however, the information-theoretic principles governing their reverse processes remain significantly less understood than those of their…

The slow inference process of image diffusion models significantly degrades interactive user experiences. To address this, we introduce Diffusion Preview, a novel paradigm employing rapid, low-step sampling to generate preliminary outputs…

Diffusion distillation is a widely used technique to reduce the sampling cost of diffusion models, yet it often requires extensive training, and the student performance tends to be degraded. Recent studies show that incorporating a GAN…

We provide the first convergence guarantees for the Consistency Models (CMs), a newly emerging type of one-step generative models that can generate comparable samples to those generated by Diffusion Models. Our main result is that, under…

Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…

Diffusion models have demonstrated significant promise in various generative tasks; however, they often struggle to satisfy challenging constraints. Our approach addresses this limitation by rethinking training-free loss-guided diffusion…

Diffusion models, such as Stable Diffusion, have shown incredible performance on text-to-image generation. Since text-to-image generation often requires models to generate visual concepts with fine-grained details and attributes specified…

We challenge a fundamental assumption of diffusion models, namely, that a large number of latent-states or time-steps is required for training so that the reverse generative process is close to a Gaussian. We first show that with careful…