DMA$^2$: Pixel-space Distribution Matching with Adversarial and Anchor Losses

Step distillation has become a leading technique for accelerating diffusion models, among which Distribution Matching Distillation (DMD) and Consistency Distillation are two representative paradigms. While consistency methods enforce self-consistency along the full PF-ODE trajectory to steer it toward the clean data manifold, vanilla DMD relies on sparse supervision at a few predefined discrete timesteps. This restricted discrete-time formulation and mode-seeking nature of the reverse KL divergence tends to exhibit visual artifacts and over-smoothed outputs, often necessitating complex auxiliary modules -- such as GANs or reward models -- to restore visual fidelity. In this work, we introduce Continuous-Time Distribution Matching (CDM), migrating the DMD framework from discrete anchoring to continuous optimization for the first time. CDM achieves this through two continuous-time designs. First, we replace the fixed discrete schedule with a dynamic continuous schedule of random length, so that distribution matching is enforced at arbitrary points along sampling trajectories rather than only at a few fixed anchors. Second, we propose a continuous-time alignment objective that performs active off-trajectory matching on latents extrapolated via the student's velocity field, improving generalization and preserving fine visual details. Extensive experiments on different architectures, including SD3-Medium and Longcat-Image, demonstrate that CDM provides highly competitive visual fidelity for few-step image generation without relying on complex auxiliary objectives. Code is available at https://github.com/byliutao/cdm.

Distributional Diffusion Models (DDMs) replace the standard mean-prediction denoiser with a \emph{distributional} denoiser trained via a scoring rule objective, learning a stochastic approximation to $p(x_1 \mid x_t)$ rather than its conditional mean. However, scaling DDMs to modern image-generation settings faces two obstacles: (i) multi-particle training incurs overhead that scales with the number of particles, (ii) DDMs use globally fixed scoring rule hyperparameters, forcing a single trade-off across sampling budgets. We mitigate these limitations by deferring particle expansion to late transformer layers, and the hyperparameter trade-off by introducing time-dependent scoring rule schedules informed by the dynamical regimes of~\citet{Biroli2024}. Combined with a DiT-based latent setup, these changes make DDM training practical on class-conditional ImageNet-$256^2$, achieving 4.48 FID at 4 steps and 2.38 at 50 steps with DiT-XL/2, from a single model trained from scratch in one stage, without a teacher, self-distillation or JVPs. The result is a stochastic few-step generator whose FID does not degrade as the sampling budget grows from 4 to 50 NFE, and the same recipe transfers to text-to-image generation. Code and pre-trained models available at https://github.com/CompVis/iDDM.

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.