Distribution Matching Distillation (DMD) distills multi-step diffusion models into few-step generators by minimizing reverse KL divergence. Despite its strong performance, DMD guides samples by local density alone, which introduces two limitations: teacher scores can be unreliable in regions of low teacher density, and the mode-seeking behavior of reverse KL can collapse the student onto a subset of the teacher modes. We first connect DMD to Wasserstein gradient flow, showing that its gradient follows from a fixed-point formulation with integral KL (IKL) as the energy functional. This perspective motivates augmenting IKL with an optimal transport term that addresses these limitations by guiding outlier samples toward the target and promoting mode coverage. We realize this term using Sinkhorn divergence estimated from finite batches. In practice, however, errors in the estimated Sinkhorn velocity can perturb in-domain samples for which IKL guidance is already accurate. To this end, we introduce sDMD, which adaptively activates the Sinkhorn correction based on discriminator outputs, focusing on outlier samples where IKL may be unreliable. With 2--4 sampling steps on FLUX.1-dev, Qwen-Image-20B, and Wan2.1-14B, sDMD outperforms distillation baselines on GenEval, DPG, WISE, and VBench while improving sample diversity over DMD2.
Xin Yang, Cai Xu, Haishun Chen, Ying Liu, Jie Zhao, Wei Zhao, Ziyu Guan
Accurate time series forecasting (TSF) is essential for Web applications, such as traffic monitoring and online resource management. Recent advances in leveraging pre-trained large language models (LLMs) have shown promising performance in TSF. However, existing LLM-based TSF methods largely optimize the overall forecasting objective while overlooking temporal pattern imbalance (TPI), where different temporal patterns occur at highly unequal frequencies. Our empirical analysis reveals that TPI is prevalent across widely used TSF benchmarks, with substantially higher forecasting errors on less frequent patterns. To address this issue, we propose IMRouter (Imbalance-aware Temporal Pattern Routing), a novel framework that mitigates TPI-induced biases in both temporal representation learning and cross-modal alignment. Specifically, IMRouter introduces Pattern-Adaptive Temporal Representation Learning (PATR), which leverages gradient conflict and local gradient density to guide expert specialization. By penalizing incompatible expert assignments with density-aware weighting, PATR reduces the dominance of frequent optimization signals in router training. Furthermore, Routing-Guided Semantic Alignment (RGSA) transfers the pattern-specific knowledge learned by the router to cross-modal alignment through mutual information maximization, preserving distinctive temporal information across different patterns. Extensive experiments on benchmark datasets demonstrate the effectiveness of IMRouter, particularly in improving forecasting performance on less frequent temporal patterns.