Related papers: Nearly $d$-Linear Convergence Bounds for Diffusion…
The denoising diffusion probabilistic model (DDPM) has emerged as a mainstream generative model in generative AI. While sharp convergence guarantees have been established for the DDPM, the iteration complexity is, in general, proportional…
This paper studies sampling error bounds for denoising diffusion probabilistic models (DDPMs) in the 2-Wasserstein distance. Our contributions are threefold. (i) Under general Lipschitz-type conditions on the score function and for a broad…
We consider the problem of estimating a $d$-dimensional discrete distribution from its samples observed under a $b$-bit communication constraint. In contrast to most previous results that largely focus on the global minimax error, we study…
We prove that $\tilde{\Theta}(k d^2 / \varepsilon^2)$ samples are necessary and sufficient for learning a mixture of $k$ Gaussians in $\mathbb{R}^d$, up to error $\varepsilon$ in total variation distance. This improves both the known upper…
Because diffusion models have shown impressive performances in a number of tasks, such as image synthesis, there is a trend in recent works to prove (with certain assumptions) that these models have strong approximation capabilities. In…
Sampling algorithms play an important role in controlling the quality and runtime of diffusion model inference. In recent years, a number of works~\cite{chen2023sampling,chen2023ode,benton2023error,lee2022convergence} have proposed schemes…
We develop a new technique for constructing sparse graphs that allow us to prove near-linear lower bounds on the round complexity of computing distances in the CONGEST model. Specifically, we show an $\widetilde{\Omega}(n)$ lower bound for…
Modern regression problems often involve high-dimensional data and a careful tuning of the regularization hyperparameters is crucial to avoid overly complex models that may overfit the training data while guaranteeing desirable properties…
Diffusion models are a new class of generative models that revolve around the estimation of the score function associated with a stochastic differential equation. Subsequent to its acquisition, the approximated score function is then…
We study sparse linear regression over a network of agents, modeled as an undirected graph and no server node. The estimation of the $s$-sparse parameter is formulated as a constrained LASSO problem wherein each agent owns a subset of the…
Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. They work by diffusing the data distribution into a Gaussian distribution and then learning to reverse this noising process to obtain…
The behavior of slow-fast diffusions as the separation of scale diverges is a well-studied problem in the literature. In this short paper, we revisit this problem and obtain a new proof of existing strong quantitative convergence estimates…
Limited by the encoder-decoder architecture, learning-based edge detectors usually have difficulty predicting edge maps that satisfy both correctness and crispness. With the recent success of the diffusion probabilistic model (DPM), we…
Diffusion models have recently achieved great success in the synthesis of high-quality images and videos. However, the existing denoising techniques in diffusion models are commonly based on step-by-step noise predictions, which suffers…
Diffusion models struggle to produce samples that respect constraints, a common requirement in scientific applications. Recent approaches have introduced regularization terms in the loss or guidance methods during sampling to enforce such…
In this paper, we study two problems: (1) estimation of a $d$-dimensional log-concave distribution and (2) bounded multivariate convex regression with random design with an underlying log-concave density or a compactly supported…
Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…
We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…
Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…
Reinforcement learning (RL) has emerged as a powerful tool for aligning diffusion models with human preferences, typically by optimizing a single reward function under a KL regularization constraint. In practice, however, human preferences…