Generative modeling can be formulated as learning a mapping $f$ such that its pushforward distribution matches the data distribution. The pushforward behavior can be carried out iteratively at inference time, for example, in diffusion/flow-based models. In this paper, we propose *Drifting Models*, a generative modeling framework that evolves the pushforward distribution during training and naturally admits one-step inference. We introduce a drifting field that governs the sample movement and achieves equilibrium when the distributions match. This leads to a training objective that allows the neural network optimizer to evolve the distribution. In experiments, our one-step generator achieves state-of-the-art results on ImageNet 256$\times$256, with FID 1.54 in latent space and 1.61 in pixel space. We hope that our work opens up new opportunities for high-quality one-step generation.

We show that Fréchet Distance (FD), long considered impractical as a training objective, can in fact be effectively optimized in the representation space. Our idea is simple: decouple the population size for FD estimation (e.g., 50k) from the batch size for gradient computation (e.g., 1024). We term this approach FD-Loss. Optimizing FD-Loss reveals several surprising findings. First, post-training a base generator with FD-Loss in different representation spaces consistently improves visual quality. Under the Inception feature space, a one-step generator achieves 0.72 FID on ImageNet $256\times256$. Second, the same FD-Loss repurposes multi-step generators into strong one-step generators without teacher distillation, adversarial training or per-sample targets. Third, FID can misrank visual quality: modern representations can yield better samples despite worse Inception FID. This motivates FDr$^{k}$, a multi-representation metric. We hope this work will encourage further exploration of distributional distances in diverse representation spaces as both training objectives and evaluation metrics for generative models. Code and checkpoints will be open-sourced.

Diffusion models generate samples by iteratively querying learned score estimates. A rapidly growing literature focuses on accelerating sampling by minimizing the number of score evaluations, yet the information-theoretic limits of such acceleration remain unclear. In this work, we establish the first score query lower bounds for diffusion sampling. We prove that for $d$-dimensional distributions, given access to score estimates with polynomial accuracy $\varepsilon=d^{-O(1)}$ (in any $L^p$ sense), any sampling algorithm requires $\widetilde{\Omega}(\sqrt{d})$ adaptive score queries. In particular, our proof shows that any sampler must search over $\widetilde{\Omega}(\sqrt{d})$ distinct noise levels, providing a formal explanation for why multiscale noise schedules are necessary in practice.

Current video-to-4D methods struggle with complex topology changes, transparent materials, thin structures, and inner surfaces. We present Trellis4D, a dynamic mesh generation framework by inheriting the expressive representation of Trellis2, adapting it from image-to-3D to video-conditioned 4D generation. Our design arises from two key questions: (a) how to enable Trellis2's frame-local attention to share information across frames while preserving its pretrained quality on rare cases such as transparent objects and inner surfaces, and (b) how to inject temporal information into a purely 3D positional encoding without breaking pretrained capabilities. We address (a) with a sliding-window cross-frame attention and anchor on the first frame. The first frame is generated by the base Trellis2 model and injected into our model, letting it inherit Trellis2's quality in rare cases through cross-frame attention. We address (b) with a 4D temporal encoding that repurposes redundant low-frequency spatial RoPE bands for time, extending the encoding from 3D with no additional parameters. Extensive experiments show the effectiveness of Trellis4D for high-quality dynamic mesh generation on ActionBench and our own challenging complex dynamics set.