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.
Abstract
Modern diffusion and flow-based models are increasingly moving toward few-step, latent-free generation to bypass the computational overhead of multi-step sampling and the reconstruction bottlenecks of external autoencoders. We propose the Interval Denoiser, a theoretically rigorous framework for latent-free generation. Derived directly from the flow matching ODE, it establishes an exact analytical mapping for intermediate trajectory states. Unlike prior formulations, our prediction is shown to reside on a low-dimensional manifold across any time interval, making the regression tractable for a network operating directly on pixels. Furthermore, by avoiding empirical algebraic substitutions, our formulation correctly isolates the pure time derivative to prevent biased gradient evaluations and ensure exact first-order optimization. By analyzing this objective, we equip our framework with residual clipping and a time-sampling curriculum, enabling effective long-interval training and improving few-step performance. Trained from scratch on ImageNet 256x256, our model achieves an FID of 4.55 in one step (1-NFE) and 3.98 in two steps (2-NFE) without perceptual losses.
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.
Diffusion models achieve impressive image-generation quality but remain expensive at inference time. Diffusion distillation reduces sampling steps, yet many distilled models, including SDXL-Lightning and distribution matching distillation methods, suffer from degraded Fr\'echet Inception Distance (FID). We analyze this phenomenon through a PAC-style generalization bound. Our analysis suggests that aggressive early-step redirection of the velocity field makes the distillation target harder to learn, enlarging the train-test gap. As a result, early-step output distributions differ between training and inference, causing distribution mismatch in the intermediate noisy latent used as next-step inputs. We empirically validate this mechanism by showing reduced diversity in both intermediate features and final outputs. To address this issue, we propose EMPURPLE, a simple training-free method that recycles intermediate latents sampled from the original model. EMPURPLE is model-agnostic and improves FID by 7\% to 20\% across DMD2, Hyper-SD, FlashSD, and SDXL-Lightning. The repo is: https://github.com/TheLovesOfLadyPurple/Empurple-Training-Free-Algorithm-To-enhance-Diversity-of-The-Diffusion-Distillation-Model
Although iterative denoising (i.e., diffusion/flow) methods offer strong generative performance, they suffer from low generation efficiency, requiring hundreds of steps of network forward passes to simulate a single sample. Mitigating this requires taking larger step-sizes during simulation, thereby allowing one- or few-step generation. Recently proposed shortcut model learns larger step-sizes by enforcing alignment between its direction and the path defined by a base many-step flow-matching model through a self-consistency loss. However, its generation quality is significantly lower than the base model. In this paper, we formulate few-step generation as a controlled base generative process, and show that self-consistency loss can be understood through the lens of optimal control. This perspective naturally motivates its generalization to the proposed cumulative self-consistency loss that cumulatively penalizes misalignment along the entire trajectory. This encourages larger step-sizes that not only align with the base model at the current time step but also support alignment in the subsequent steps, facilitating high-quality generation. Furthermore, we draw a connection between our approach and reinforcement learning, potentially opening the door to a new set of approaches for few-step generation. Experiments show that we significantly improve one- and few-step generation quality under the same training budget. Implementation is available at: https://github.com/paribeshregmi/Shortcut-CSL
Paribesh Regmi, S. Ghimire, Rui Li· International Conference on...· 0 citations
A novel post-training acceleration framework that exploits this redundancy by integrating dynamic structural sparsification directly into the distillation process, and introduces a Progressive Training Strategy coupled with an Output Rollout Mechanism that ensures the coherent learning of structural decisions across timesteps.
Yu Cheng, Siyue Yao, Zhongang Qi et al.· 0 citations
Autoregressive video diffusion models have enabled the generation of arbitrarily long videos by removing conditioning on future frames, thus greatly improving computational efficiency. Yet, they suffer from error accumulation over time, as the denoised sequence gradually drifts away from the conditioning distribution seen during training. Recent advances attempt to reduce this error by anchoring each generated frame to the learned manifold of real ones. However, even when all generated individual frames lie close to the real manifold, there are trajectories which the model lacks sufficient knowledge to continue without exiting it, thus reaching a terminal point. To prevent the model from being trapped in terminal points, we start from the hypothesis that for well-modeled future trajectories the distribution of the predicted noise should match the one of the forward noising process. To enforce such a prior at test time, we introduce Terminal points Avoidance through Noise Guided Optimization (TANGO), which uses the diffusion model as a critic of its own outputs, by predicting one step forward and requiring an isotropic Gaussian noise prediction. We use the deviation from this expected noise distribution to search for an alternative trajectory that does not lead to a terminal point. Our approach achieves a $3.1\%$ absolute improvement on VBench over state-of-the-art, while reducing Fr\'echet Video Distance by $28.3\%$ on average across $15$s videos. Our code is available on https://mever-team.github.io/tango.
Dimitrios Karageorgiou, Symeon Papadopoulos, Ioannis Kompatsiaris et al.· 0 citations
Diffusion-based super-resolution (SR) achieves strong perceptual quality but requires costly iterative denoising. Existing one-step distillation methods reduce inference time but depend on expensive pretrained teachers, whereas CTMSR avoids distillation through PF-ODE consistency training yet does not explicitly model the restoration dynamics from low-resolution (LR) inputs to high-resolution (HR) images. We propose MeanSR, a one-step perceptual SR method that learns an LR-conditioned average velocity field to directly capture the finite-time transition from degraded or noisy inputs to plausible HR outputs. We further reformulate distribution trajectory matching for average-velocity generation and introduce a Stage-Aware Temporal Sampling strategy to improve trajectory learning. Experiments on synthetic and real-world benchmarks show that MeanSR outperforms CTMSR on CLIPIQA, MUSIQ, and MANIQA while substantially reducing FLOPs and inference latency. MeanSR also reconstructs sharper structures and more realistic textures with fewer perceptual artifacts.
Axi Niu, Jiawei Kou, Kang Zhang et al.· 0 citations