8 accepted papers
Recently, diffusion models have achieved a great performance with a small dataset of size $n$ and a fast optimization process. Despite the impressive performance, the estimation error suffers from the curse of dimensionality $n^{-1/D}$, where $D$ is the data dimension. Since images are usually a un…
Consistency models, a new class of one-step generative models, have shown competitive performance with multi-step diffusion models. The most challenging part of consistency models is the training process, which discretizes the continuous diffusion process into $K$ steps and trains a one-step mapping…
Recently, variance exploding (VE) diffusion models have achieved state-of-the-art (SOTA) performance in two implementations: (1) the SDE-based implementation and (2) the probability flow ODE (PFODE) implementation. However, only a few works analyze the iteration complexity of VE-based models, and mo…
While diffusion models have demonstrated impressive performance, there is a growing need for generating samples tailored to specific user-defined concepts. The customized requirements promote the development of few-shot diffusion models, which use limited $n_{ta}$ target samples to fine-tune a pre-t…
Variance exploding (VE) based diffusion models, an important class of diffusion models, have shown state-of-the-art (SOTA) performance. However, only a few theoretical works analyze VE-based models, and those works suffer from a worse forward convergence rate $1/\text{poly}(T)$ than the $\exp{(-T)}$…
We study reinforcement learning (RL) with linear function approximation, unknown transition, and adversarial losses in the bandit feedback setting. Specifically, the unknown transition probability function is a linear mixture model \citep{AyoubJSWY20,ZhouGS21,HeZG22} with a given feature mapping, an…
In this work, we study the low-rank MDPs with adversarially changed losses in the full-information feedback setting. In particular, the unknown transition probability kernel admits a low-rank matrix decomposition \citep{REPUCB22}, and the loss functions may change adversarially but are revealed to t…
Self-supervised learning (SSL) has empirically shown its data representation learnability in many downstream tasks. There are only a few theoretical works on data representation learnability, and many of those focus on final data representation, treating the nonlinear neural network as a ``black box…