Discrete Meanflow Training Curriculum

Timestep sampling $p(t)$ is a central design choice in Flow Matching models, yet common practice increasingly favors static middle-biased distributions (e.g., Logit-Normal). We show that this choice induces a speed--quality trade-off: middle-biased sampling accelerates early convergence but yields worse asymptotic fidelity than Uniform sampling. By analyzing per-timestep training losses, we identify a U-shaped difficulty profile with persistent errors near the boundary regimes, implying that under-sampling the endpoints leaves fine details unresolved. Guided by this insight, we propose Curriculum Sampling, a two-phase schedule that begins with middle-biased sampling for rapid structure learning and then switches to Uniform sampling for boundary refinement. On CIFAR-10, Curriculum Sampling improves the best FID from $3.85$ (Uniform) to $3.22$ while reaching peak performance at $100$k rather than $150$k training steps. Our results highlight that timestep sampling should be treated as an evolving curriculum rather than a fixed hyperparameter.

Training fast generators on new domains with limited data remains challenging for two reasons. First, adapting a pretrained diffusion or flow model to a new domain leaves its costly multi-step sampling unaddressed, and existing acceleration methods are tied to the source parameterization--$ε$, $x$, $v$, or $u$--leaving heterogeneous pretrained models with no common acceleration target. Second, while adversarial refinement is proven effective for few-step quality, it is formulated only for instantaneous-velocity flows, not for the finite-interval average velocities that MeanFlow (MF) models predict. We address both problems. We propose MeanFlow-Transfer, which maps heterogeneous source outputs into a shared velocity representation, uses it to initialize an MF generator from the source weights, and optimizes an MF objective on the target domain. This unifies adaptation and acceleration in a single training loop across a broad range of pretrained models. We then introduce Continuous Adversarial MeanFlow, a post-training stage that extends continuous adversarial flow models from instantaneous velocities to MF's finite-interval average velocities. CAMF contrasts changes in a learned potential between real and predicted interval endpoints, recovering fine detail that MF regression averages away, and reduces to the instantaneous criterion in the vanishing-interval limit. Adapting four ImageNet-based source models--DiT ($ε$), SiT ($v$), JiT ($x$), iMF ($u$)--to five target domains, MF-T with CAMF matches or exceeds the fine-tuned teacher in FID and FDD at up to $125\times$ fewer Neural Function Evaluations (NFEs), while CAMF improves MF-T's few-step FID by $29\%$ on average.

Diffusion models and flow-based methods have shown impressive generative capability, especially for images, but their sampling is expensive because it requires many iterative updates. We introduce W-Flow, a framework for training a generator that transforms samples from a simple reference distribution into samples from a target data distribution in a single step. This is achieved in two steps: we first define an evolution from the reference distribution to the target distribution through a Wasserstein gradient flow that minimizes an energy functional; second, we train a static neural generator to compress this evolution into one-step generation. We instantiate the energy functional with the Sinkhorn divergence, which yields an efficient optimal-transport-based update rule that captures global distributional discrepancy and improves coverage of the target distribution. We further prove that the finite-sample training dynamics converge to the continuous-time distributional dynamics under suitable assumptions. Empirically, W-Flow sets a new state of the art for one-step ImageNet 256$\times$256 generation, achieving 1.29 FID, with improved mode coverage and domain transfer. Compared to multi-step diffusion models with similar FID scores, our method yields approximately 100$\times$ faster sampling. These results show that Wasserstein gradient flows provide a principled and effective foundation for fast and high-fidelity generative modeling.