This appendix is organized as follows: Section A: the detailed dataset statistics and a summary of model properties w.r.t. We present the details on each dataset in Table 4. Under the online continual setting, the tasks are observed following a fixed order and the data from each task is observed as a (one-pass) stream of samples. The batch size is 10 for all the datasets. We do not randomize the order of tasks or optimize the task orders.

Text-to-Image diffusion models have made tremendous progress over the past two years, enabling the generation of highly realistic images based on open-domain text descriptions. However, despite their success, text descriptions often struggle to adequately convey detailed controls, even when composed of long and complex texts. Moreover, recent studies have also shown that these models face challenges in understanding such complex texts and generating the corresponding images. Therefore, there is a growing need to enable more control modes beyond text description. In this paper, we introduce Uni-ControlNet, a unified framework that allows for the simultaneous utilization of different local controls (e.g., edge maps, depth map, segmentation masks) and global controls (e.g., CLIP image embeddings) in a flexible and composable manner within one single model. Unlike existing methods, Uni-ControlNet only requires the fine-tuning of two additional adapters upon frozen pre-trained text-to-image diffusion models, eliminating the huge cost of training from scratch. Moreover, thanks to some dedicated adapter designs, Uni-ControlNet only necessitates a constant number (i.e., 2) of adapters, regardless of the number of local or global controls used. This not only reduces the fine-tuning costs and model size, making it more suitable for real-world deployment, but also facilitate composability of different conditions. Through both quantitative and qualitative comparisons, Uni-ControlNet demonstrates its superiority over existing methods in terms of controllability, generation quality and composability.

Predicted sequences of a moving pendulum conditioned on z1 q(z1|x1:5,u1:4) or, in case of the EKVAE, on z1 p(z1|a1:5,u1:4), where the auxiliary variables are obtained through a1:5 q(a1:5|x1:5). The average prediction accuracy, measured by the MSE, can be found in Tab.

Organization: This supplementary material is presented in a format parallel to the main paper. The section numbers and titles are consistent with the main paper. But, here we also add one new section: Section 10 where we describe the societal impacts and possible negative impacts of the paper. Similarly, the Theorem numbers are consistent with the main paper, but we also have several additional theorems and lemmas which were not included in the main paper. GAN-type Objective for KLEstimation Let f be a discriminator, f: X IR. Let p(x) and q(x) be two probability density functions defined over the space X.