Continuous Adversarial Flow Models

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.

Post-training of flow matching models-aligning the output distribution with a high-quality target-is mathematically equivalent to imitation learning. While Supervised Fine-Tuning mimics expert demonstrations effectively, it cannot correct policy drift in unseen states. Preference optimization methods address this but require costly preference pairs or reward modeling. We propose Flow Matching Adversarial Imitation Learning (FAIL), which minimizes policy-expert divergence through adversarial training without explicit rewards or pairwise comparisons. We derive two algorithms: FAIL-PD exploits differentiable ODE solvers for low-variance pathwise gradients, while FAIL-PG provides a black-box alternative for discrete or computationally constrained settings. Fine-tuning FLUX with only 13,000 demonstrations from Nano Banana pro, FAIL achieves competitive performance on prompt following and aesthetic benchmarks. Furthermore, the framework generalizes effectively to discrete image and video generation, and functions as a robust regularizer to mitigate reward hacking in reward-based optimization. Code and data are available at https://github.com/HansPolo113/FAIL.

Pixel-space generative models bypass lossy latent compression, yet necessitate joint learning of global structure and fine-grained details in a high-dimensional space. Standard flow matching interpolates noise toward a fixed clean-image endpoint, leaving the spectral evolution to be learned implicitly. In this paper, we introduce Energy-Guided Flow Matching(EG-FM) that explicitly models a coarse-to-fine generative trajectory by moving endpoint. Specifically, EG-FM replaces the fixed endpoint with a heat-kernel-filtered endpoint that evolves smoothly from low-frequency image to clean image. The fraction of high-frequency signal in moving endpoint is released by an image-specific energy-guided scheduling, leading to the re-targeting of velocity in flow matching. Our framework requires no adaptation of the backbone and training data, bringing negligible cost on the training and inference stages. In our experiment, EG-FM consistently achieves lower FID on the ImageNet class-conditional image generation task at $256 \times 256$ with fewer epochs, reaching an FID of 1.55 at 200 epochs and 1.45 at 600 epochs. We continue training the generation task on the setting of $512 \times 512$ resolution, yielding a FID of 1.58 after only 40 high-resolution adaptation epochs. Furthermore, we transfer EG-FM on text-to-image generation and achieve 0.85 on GenEval score and 83.9 on DPG-Bench. Code is available at https://github.com/ysng123/EG-FM.