Related papers: Diffusion Models and the Manifold Hypothesis: Log-…

Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from…

Diffusion models have emerged as the principal paradigm for generative modeling across various domains. During training, they learn the score function, which in turn is used to generate samples at inference. They raise a basic yet unsolved…

Diffusion policies have shown impressive results in robot imitation learning, even for tasks that require satisfaction of kinematic equality constraints. However, task performance alone is not a reliable indicator of the policy's ability to…

Recent advances in diffusion models have demonstrated their remarkable ability to capture complex image distributions, but the geometric properties of the learned data manifold remain poorly understood. We address this gap by introducing a…

In this work, we study the generalizability of diffusion models by looking into the hidden properties of the learned score functions, which are essentially a series of deep denoisers trained on various noise levels. We observe that as…

Score-based diffusion models synthesize samples by reversing a stochastic process that diffuses data to noise, and are trained by minimizing a weighted combination of score matching losses. The log-likelihood of score-based diffusion models…

Score-based diffusion modeling is a generative machine learning algorithm that can be used to sample from complex distributions. They achieve this by learning a score function, i.e., the gradient of the log-probability density of the data,…

Score-based diffusion models generate new samples by learning the score function associated with a diffusion process. While the effectiveness of these models can be theoretically explained using differential equations related to the…

We present an adaptive regularization algorithm that can be effectively applied to the optimization problem in deep learning framework. Our regularization algorithm aims to take into account the fitness of data to the current state of model…

Diffusion models are extensively used for modeling image priors for inverse problems. We introduce \emph{Diff-Unfolding}, a principled framework for learning posterior score functions of \emph{conditional diffusion models} by explicitly…

Real-world datasets are inherently heterogeneous, yet how per-class structural differences and sampling imbalance shape the training dynamics of diffusion models-and potentially exacerbate disparities-remains poorly understood. While models…

Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…

We theoretically investigate the phenomena of generalization and memorization in diffusion models. Empirical studies suggest that these phenomena are influenced by model complexity and the size of the training dataset. In our experiments,…

In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often…

The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…

Diffusion models have successfully been applied to generative tasks in various continuous domains. However, applying diffusion to discrete categorical data remains a non-trivial task. Moreover, generation in continuous domains often…

Diffusion models have demonstrated empirical successes in various applications and can be adapted to task-specific needs via guidance. This paper studies a form of gradient guidance for adapting a pre-trained diffusion model towards…

Diffusion models have shown remarkable success across a wide range of generative tasks. However, they often suffer from spatially inconsistent generation, arguably due to the inherent locality of their denoising mechanisms. This can yield…

Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…