Colorization is a crucial but labor-intensive and time-consuming process of animation production. The automation of animation line-drawing colorization has become a prominent research topic. Recently, methods based on pre-trained text-to-image models have been explored for the task of line-drawing colorization. However, these approaches may result in colorization errors when dealing with complex situations such as positional changes and extensive motion commonly encountered in animated scenes. These issues are primarily attributed to the inadequate semantic correspondence between the reference images and line-drawings. To tackle this problem, we introduce the Animation Anycolor framework. This approach leverages spatial attention mechanisms to integrate the appearance features of reference images, ensuring consistent feature transmission. Furthermore, we present a novel technique that employs keypoint matching to explicitly direct the network to recognize the feature correspondence areas between reference and target images, thus effectively mitigating color confusion. Our method preserves the accuracy and naturalness of color results in scenes characterized by positional shifts and character movement. Comparative evaluations indicate that our method outperforms the baseline by an average of 11.3% on the FID metric. Notably, this method improves the efficiency of line-drawing colorization and reduces production costs. It also introduces new insights by combining in-context correspondences with knowledge from the pre-trained model. This approach has broad application prospects in the animation industry.

Animation colorization plays a vital role in animation production, yet existing methods struggle to achieve color accuracy and temporal consistency. To address these challenges, we propose AnimeColor, a novel reference-based animation colorization framework leveraging Diffusion Transformers (DiT). Our approach integrates sketch sequences into a DiT-based video diffusion model, enabling sketch-controlled animation generation. We introduce two key components: a High-level Color Extractor (HCE) to capture semantic color information and a Low-level Color Guider (LCG) to extract fine-grained color details from reference images. These components work synergistically to guide the video diffusion process. Additionally, we employ a multi-stage training strategy to maximize the utilization of reference image color information. Extensive experiments demonstrate that AnimeColor outperforms existing methods in color accuracy, sketch alignment, temporal consistency, and visual quality. Our framework not only advances the state of the art in animation colorization but also provides a practical solution for industrial applications. The code will be made publicly available at https://github.com/IamCreateAI/AnimeColor.

Lower bounds for the Rényi entropies of sums of independent random variables taking values in cyclic groups of prime order under permutations are established. The main ingredients of our approach are extended rearrangement inequalities in prime cyclic groups building on Lev [ Duke Math. J., 107 (2001), pp. 239--263] and notions of stochastic ordering. Several applications are developed, including to discrete entropy power inequalities, the Littlewood--Offord problem, and counting solutions of certain linear systems.

A simple new lower bound is provided for the Rényi entropy of the convolution of probability distributions on the integers in terms of certain (discrete) rearrangements of these distributions. This inequality may be thought of as an entropy power inequality for integer-valued random variables.

A lower bound on the Rényi differential entropy of a sum of independent random vectors is demonstrated in terms of rearrangements. For the special case of Boltzmann-Shannon entropy, this lower bound is better than that given by the entropy power inequality. Several applications are discussed, including a new proof of the classical entropy power inequality and an entropy inequality involving symmetrization of Lévy processes.

A new lower bound on the entropy of the sum of independent random vectors is demonstrated in terms of rearrangements. This lower bound is better than that given by the entropy power inequality. In fact, we use it to give a new, independent, and simple proof of the entropy power inequality in the case when the summands are identically distributed. We also give a more involved but new way to recover the full entropy power inequality, without invoking Fisher information, MMSE or any differentiation of information functionals.