To mitigate the time complexity of generative models, one-step generative models have recently emerged through direct mapping from noise to data in a single forward pass. However, the reward-guided fine-tuning method of one-step generative models remains largely unexplored. To address this, we consider one-step generators from an optimal transport view, investigating Wasserstein Gradient Flow (WGF) for modeling smooth and controlled distributional evolution in probability space. We then propose a novel reward-guided fine-tuning of a one-step generative model via WGF. We derive a practical training method that requires no reward gradients, thereby handling both non-differentiable and differentiable rewards. Moreover, our method provides smooth and stable reward-guided distributional updates while mitigating reward hacking and mode collapse. Experiments on 2D synthetic data, CIFAR-10, and ImageNet 256×256 with diverse rewards, including JPEG (in)compressibility, class probability, Black-and-White and CLIP alignment, show that our method achieves better reward alignment compared to baselines.
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 256×256 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× faster sampling. These results show that Wasserstein gradient flows provide a principled and effective foundation for fast and high-fidelity generative modeling.
Reward fine-tuning aims to update a pre-trained flow-based generative model to improve the downstream reward of its generated samples. Existing methods typically formulate this problem as sampling from a reward-tilted distribution, the solution to a KL-regularized reward-maximization problem. Here, we introduce an optimal transport regularizer built directly from the pre-trained drift. Unlike KL reward tilting, the resulting objective transports individual samples toward higher reward rather than reweighting the base distribution. We show that the resulting problem is equivalent to a deterministic optimal control problem on the flow. Given a pre-trained flow map, this equivalence yields a simulation-free reinforcement learning algorithm for fine-tuning generative flows. We call the resulting framework Wasserstein-Tilted Flow Maps (WTF), the first end-to-end fine-tuning recipe native to flow maps. The output is a fine-tuned flow map that retains strong reward-aligned performance at few-step inference budgets without post-hoc distillation. Experiments on ImageNet-256 and text-to-image show that WTF achieves higher reward with comparable or higher diversity than baselines, while requiring up to 280× less training compute. More broadly, we argue that accelerated samplers such as flow maps are essential infrastructure for efficient post-training, and that the dominant KL-regularized formulation is only one of many choices worth revisiting.
Recent advances in few-step diffusion distillation have enabled efficient image generation, yet aligning these models with human preferences remains challenging. We propose Reward-Tilted Distribution Matching Distillation (RTDMD), a two-stage framework that unifies distribution matching distillation with reward-guided reinforcement learning for few-step flow generators. We show that minimizing the KL divergence to a reward-tilted teacher distribution naturally decomposes into a distribution matching term and a reward maximization term. In the first stage, we introduce Ambient-Consistent Distribution Matching Distillation (AC-DMD), which performs subinterval-wise distribution matching and augments the fake score objective with a consistency regularizer to help the fake score model track the shifting generator distribution under limited updates. In the second stage, we jointly optimize both terms: for the reward maximization term, we derive a hybrid policy gradient that combines a GRPO-style estimator for the stochastic intermediate transitions with direct reward backpropagation through the deterministic final step, and further introduce step-subset GRPO (SubGRPO) to reduce variance. Experiments on SD3, SD3.5, and FLUX.2 demonstrate that RTDMD establishes new state-of-the-art results across preference, aesthetic, and compositional metrics with only 4 inference steps, outperforming previous few-step text-to-image generation methods. Code and models are available at https://github.com/Harahan/RTDMD.