Yong Zhang

Minghong Cai, Xiaodong Cun, Xiaoyu Li et al.

Sora-like video generation models have achieved remarkable progress with a Multi-Modal Diffusion Transformer MM-DiT architecture. However, the current video generation models predominantly focus on single-prompt, struggling to generate coherent scenes with multiple sequential prompts that better reflect real-world dynamic scenarios. While some pioneering works have explored multi-prompt video generation, they face significant challenges including strict training data requirements, weak prompt following, and unnatural transitions. To address these problems, we propose DiTCtrl, a training-free multi-prompt video generation method under MM-DiT architectures for the first time. Our key idea is to take the multi-prompt video generation task as temporal video editing with smooth transitions. To achieve this goal, we first analyze MM-DiT's attention mechanism, finding that the 3D full attention behaves similarly to that of the cross/self-attention blocks in the UNet-like diffusion models, enabling mask-guided precise semantic control across different prompts with attention sharing for multi-prompt video generation. Based on our careful design, the video generated by DiTCtrl achieves smooth transitions and consistent object motion given multiple sequential prompts without additional training. Besides, we also present MPVBench, a new benchmark specially designed for multi-prompt video generation to evaluate the performance of multi-prompt generation. Extensive experiments demonstrate that our method achieves state-of-the-art performance without additional training.

Zhaosong Lu, Yong Zhang

In this paper we consider sparse approximation problems, that is, general $l_0$ minimization problems with the $l_0$-"norm" of a vector being a part of constraints or objective function. In particular, we first study the first-order optimality conditions for these problems. We then propose penalty decomposition (PD) methods for solving them in which a sequence of penalty subproblems are solved by a block coordinate descent (BCD) method. Under some suitable assumptions, we establish that any accumulation point of the sequence generated by the PD methods satisfies the first-order optimality conditions of the problems. Furthermore, for the problems in which the $l_0$ part is the only nonconvex part, we show that such an accumulation point is a local minimizer of the problems. In addition, we show that any accumulation point of the sequence generated by the BCD method is a saddle point of the penalty subproblem. Moreover, for the problems in which the $l_0$ part is the only nonconvex part, we establish that such an accumulation point is a local minimizer of the penalty subproblem. Finally, we test the performance of our PD methods by applying them to sparse logistic regression, sparse inverse covariance selection, and compressed sensing problems. The computational results demonstrate that our methods generally outperform the existing methods in terms of solution quality and/or speed.