Characterizing Motion Encoding in Video Diffusion Timesteps

Text-to-video diffusion models synthesize temporal motion and spatial appearance through iterative denoising, yet how motion is encoded across timesteps remains poorly understood. Practitioners often exploit the empirical heuristic that early timesteps mainly shape motion and layout while later ones refine appearance, but this behavior has not been systematically characterized. In this work, we proxy motion encoding in video diffusion timesteps by the trade-off between appearance editing and motion preservation induced when injecting new conditions over specified timestep ranges, and characterize this proxy through a large-scale quantitative study. This protocol allows us to factor motion from appearance by quantitatively mapping how they compete along the denoising trajectory. Across diverse architectures, we consistently identify an early, motion-dominant regime and a later, appearance-dominant regime, yielding an operational motion-appearance boundary in timestep space. Building on this characterization, we simplify current one-shot motion customization paradigm by restricting training and inference to the motion-dominant regime, achieving strong motion transfer without auxiliary debiasing modules or specialized objectives. Our analysis turns a widely used heuristic into a spatiotemporal disentanglement principle, and our timestep-constrained recipe can serve as ready integration into existing motion transfer and editing methods.

Dense Backpropagation Improves Training for Sparse Mixture-of-Experts

Mixture of Experts (MoE) pretraining is more scalable than dense Transformer pretraining, because MoEs learn to route inputs to a sparse set of their feedforward parameters. However, this means that MoEs only receive a sparse backward update, leading to training instability and suboptimal performance. We present a lightweight approximation method that gives the MoE router a dense gradient update while continuing to sparsely activate its parameters. Our method, which we refer to as Default MoE, substitutes missing expert activations with default outputs consisting of an exponential moving average of expert outputs previously seen over the course of training. This allows the router to receive signals from every expert for each token, leading to significant improvements in training performance. Our Default MoE outperforms standard TopK routing in a variety of settings without requiring significant computational overhead. Code: https://github.com/vatsal0/default-moe.