Energy-Guided Flow Matching is introduced that explicitly models a coarse-to-fine generative trajectory by moving endpoint that evolves smoothly from low-frequency image to clean image and requires no adaptation of the backbone and training data.
Abstract
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.
Residual Flow Matching for Image Super-Resolution (RFMSR) is proposed, a vision-only framework that centers the source distribution at the LQ latent, reducing transport distance and preserving structural priors throughout the flow trajectory.
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This work proposes Projected Energy Matching, a scalable framework that resolves structural and computational bottlenecks in energy matching, and introduces Helmholtz Distillation, a structural relaxation that leverages a Hutchinson trace estimator to explicitly absorb rotational noise into an auxiliary residual network.
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The Interval Denoiser, a theoretically rigorous framework for latent-free generation, derived directly from the flow matching ODE, establishes an exact analytical mapping for intermediate trajectory states and is shown to reside on a low-dimensional manifold across any time interval.
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We propose Perceptual Flow Matching (PFM), a simple yet effective framework for few-step generation in flow-matching models. Rather than performing velocity regression in the conventional VAE latent space, PFM supervises flow matching in a perceptual feature space using pretrained perceptual models. This simple change substantially improves the few-step generation capability of flow-matching models, reducing the number of sampling steps from 35-50 to 4-8 while preserving generation quality. Unlike existing acceleration and distillation approaches, PFM requires neither teacher models nor auxiliary score networks and can be integrated into standard flow-matching training pipelines with minimal modifications. Extensive experiments on image generation, video generation, and image editing tasks demonstrate that PFM consistently produces high-quality results while producing fewer artifacts than existing distillation-based methods. We further show that perceptual supervision shifts the regression minimizer from mean-seeking to mode-seeking, biasing predictions toward on-manifold modes that remain accurate under coarse few-step integration. Our results reveal that standard flow-matching training can naturally yield high-quality few-step generators when supervised in an appropriate representation space. We hope this insight inspires future research into representation-aware objectives for efficient generative modeling.
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The results show that careful tokenizer--backbone--system co-design can deliver strong high-resolution generation and editing within an efficient 4B model family.
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It is shown in this work that flow matching models with a potential-induced velocity yield an explicit scalar energy at all transport times, whose gradient is exactly the converted learned score and which recovers the marginal negative log-density at the population optimum.
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