Consistency distillation has significantly accelerated diffusion-model inference, but its sampling dynamics remain underexplored. We reveal an asymmetry: although Logit-Normal sampling priors work well for standard iterative generation, consistency distillation exhibits a different difficulty profile (e.g., U-shaped), with optimization bottlenecks concentrated at the boundary stages rather than intermediate steps. To address the limitations of static sampling under evolving learning demands, we propose Curvature-Adaptive Consistency Flow Matching (CACFM). By formulating distillation as a dynamic decision process, CACFM uses a lightweight reinforcement learning agent to probe Probability Flow ODE trajectories and construct an efficiency-oriented curriculum that prioritizes critical regions without manual scheduling. Combined with Flow-adapted DMD and adversarial consistency objectives, our RL-based scheduler achieves state-of-the-art results on large-scale models such as FLUX and SDXL, mitigating structural deformities and preserving high-frequency details in extreme few-step regimes.
The slow iterative sampling nature remains a major bottleneck for the practical deployment of diffusion and flow-based generative models. While consistency models (CMs) represent a state-of-the-art distillation-based approach for efficient generation, their large-scale application is still limited by two key issues: training instability and inflexible sampling. Existing methods seek to mitigate these problems through architectural adjustments or regularized objectives, yet overlook the critical reliance on trajectory selection. In this work, we first conduct an analysis on these two limitations: training instability originates from loss divergence induced by unstable self-supervised term, whereas sampling inflexibility arises from error accumulation. Based on these insights and analysis, we propose the Dual-End Consistency Model (DE-CM) that selects vital sub-trajectory clusters to achieve stable and effective training. DE-CM decomposes the PF-ODE trajectory and selects three critical sub-trajectories as optimization targets. Specifically, our approach leverages continuous-time CMs objectives to achieve few-step distillation and utilizes flow matching as a boundary regularizer to stabilize the training process. Furthermore, we propose a novel noise-to-noisy (N2N) mapping that can map noise to any point, thereby alleviating the error accumulation in the first step. Extensive experimental results show the effectiveness of our method: it achieves a state-of-the-art FID score of 1.70 in one-step generation on the ImageNet 256x256 dataset, outperforming existing CM-based one-step approaches.
Diffusion and flow-matching models scale because pretraining is supervised regression: a clean sample is noised analytically, and a model regresses against a closed-form target. RL post-training aligns the model with a reward. In image generation, this makes samples compose objects correctly, render text legibly, and match human preferences. Existing methods rely on costly SDE rollouts, reward gradients, or surrogate losses, sacrificing pretraining's regression structure. We show that the structure extends to RL post-training. Under KL-regularized reward maximization, the optimal generative process tilts the clean-endpoint distribution towards samples with higher reward and leaves the noising law unchanged. Combining this with the adjoint-matching optimality condition and a REINFORCE identity, we derive Reinforce Adjoint Matching (RAM): a consistency loss that corrects the pretraining target with the reward. At each step, we draw a clean endpoint from the current model, evaluate its reward, noise it as in pretraining, and regress. No SDE rollouts, backward adjoint sweeps, or reward gradients are required. Like the pretraining objective, RAM is simple and scales. On Stable Diffusion 3.5M, RAM achieves the highest reward on composability, text rendering, and human preference, reaching Flow-GRPO's peak reward in up to 50× fewer training steps.
Andreas Bergmeister, Stefanie Jegelka, Nikolas Nüsken +2
Flow Matching models have demonstrated strong performance across a wide range of generative tasks. However, their reliance on ODE-based iterative sampling incurs substantial computational overhead in inference, which limits their applicability in real-time scenes. While distillation is a promising solution, existing approaches largely borrow from diffusion-based score matching, often failing to exploit the intrinsic geometric structure of flows and suffering from training instability, high variance, and degraded generation quality. In this paper, we propose Mean Flow Distillation (MFD), a novel distillation framework tailored for flow matching models. We theoretically demonstrate that MFD acts as a temporal low-pass filter, effectively suppressing the high-frequency optimization noise inherent in variational score distillation (VSD) while ensuring global trajectory consistency. We further prove the Mean Flow Matching Theorem, establishing that matching expected average velocities is sufficient for strict distribution alignment. Empirically, on challenging tasks of high-dimensional manifolds including 4D occupancy forecasting and text-to-image generation, MFD achieves state-of-the-art performance, enabling high-fidelity single-step generation.