Title: Mean Flows for One-step Generative Modeling
Venue: NeurIPS 2025
Accepted: yes
Keywords: Generative Models
Abstract: We propose a principled and effective framework for one-step generative modeling. We introduce the notion of average velocity to characterize flow fields, in contrast to instantaneous velocity modeled by Flow Matching methods. A well-defined identity between average and instantaneous velocities is derived and used to guide neural network training. Our method, termed the \textit{MeanFlow} model, is self-contained and requires no pre-training, distillation, or curriculum learning. MeanFlow demonstrates strong empirical performance: it achieves an FID of 3.43 with a single function evaluation (1-NFE) on ImageNet 256$\times$256 trained from scratch, significantly outperforming previous state-of-the-art one-step diffusion/flow models. Our study substantially narrows the gap between one-step diffusion/flow models and their multi-step predecessors, and we hope it will motivate future research to revisit the foundations of these powerful models.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes to directly parameterize the network to output the mean velocity of a displacement map, and uses fundamental theorem of calculus to constrain the derivative of the mean velocity to match that of the flow-matching conditional velocity. The method leverages JVP to compute the time derivative w.r.t. the model, and uses the conditional velocity $v_t$ as supervision signal for JVP calculation.\n\nSTRENGTHS AND WEAKNESSES:\nThe paper are notable in several aspects ranging from formulation to empirical results, listed below\n1. MeanFlow proposes a simple single loss, which reduces to the vanilla flow matching objective when $t=r$. The conception simplicity is easy to grasp and the L2 loss/stop-gradient makes it stable for optimization.\n2. It achieves strong 1-step FID training from scratch. \n\nHowever, I have major concerns in its exposition in relation to many related works.\n1. To my understanding, this mean field formulation is equivalent to continuous-time consistency models [1] maybe generalizing it to the consistency trajectory case. Specifically, the authors define the flow map as the 2-time indexed Euler sampler $f_\\theta(x_t,t,r) = x_t + (r-t)u_\\theta(x_t,t,r)$ and set it equal to the ODE integral of groundtruth flow $x_t + \\int_t^r u_\\tau d\\tau$. Then, time-derivative is taken on both sides so that $\\frac{d}{dt}f_\\theta(x_t,t,r) = 0$. This is exactly the same as continuous-time consistency model objective where you want to penalize $||\\frac{d}{dt}f_\\theta(x_t,t,r) ||^2$. This formulation is similarly discussed in [2], which explicitly uses a 2-time indexed version. Furthermore, the parameterization used in this paper is Euler sampler, which is a special case of flow maps in general. I feel that such connections with the previous works are inadequately discussed, and by avoiding these discussions the novelty of this work is somewhat intentionally inflated.\n\n2. The time derivative of the flow map, $u_t - u_\\theta(x_t,t,r) + (r-t)[\\frac{\\partial}{\\partial x_t} u_\\theta(x_t,t,r)^T u_t + \\frac{\\partial}{\\partial t} u_\\theta(x_t,t,r) ]$, contains the marginal velocity $u_t$. However, the authors simply substitutes $u_t$ with the conditional velocity $v_t$ without justification. Importantly, this is also equivalent to the proposal of continuous-time consistency models trained from scratch which has already proposed the stop-gradient trick to stablize training. Directly substituting $u_t$ with $v_t$ also breaks the theoretically soundness of the approach, as discussed in [2] in detail, because the two objectives (with $u_t$ and with $v_t$) are NOT equivalent in expectation over the training distribution. The authors are encouraged to justify this choice. I suppose that this discrepancy is also why stop-gradient needs to be employed, because enabling gradient through the JVP path results in minimizing an improper objective.\n\n3. Stop-gradient also makes the objective less theoretically sound because it's difficult to prove its attractivenss towards the groundtruth marginal flow map [2].\n\n4. This paper also seem to intentionally avoid comparing with few-step performance given that it naturally employs a jumping capability from any time t to any time r. Does the performance improve with more steps? If so, why not compare with other types of methods with one- and few-step capabilities such as diffusion pre-training + distillation [3-5] and autoregressive models (VAR [6]). The authors seem to avoid comparing with the best results achieved by other models which can be misleading for the community.\n\n5. Besides stop-gradient, the paper also proposes other tricks such as adaptive weighting, which amounts to minimizing L1 or Pseudo-huber loss. This makes the optimum of the new objective even less clear for analysis. If only L2 is used, what is the performance of the XL model? Is there a noticeable gap? How much does the adaptive weighting affect the best performance (this gap is not clear from the ablation study)\n\n\n\n[1] Lu, Cheng, and Yang Song. \"Simplifying, stabilizing and scaling continuous-time consistency models.\" arXiv preprint arXiv:2410.11081 (2024).\n\n[2] Boffi, Nicholas M., Michael S. Albergo, and Eric Vanden-Eijnden. \"Flow Map Matching.\" arXiv preprint arXiv:2406.07507 (2024).\n\n[3] Yin, Tianwei, et al. \"One-step diffusion with distribution matching distillation.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2024.\n\n[4] Zhou, Mingyuan, et al. \"Score identity distillation: Exponentially fast distillation of pretrained diffusion models for one-step generation.\" Forty-first International Conference on Machine Learning. 2024.\n\n[5] Zhou, Mingyuan, et al. \"Adversarial Score identity Distillation: Rapidly Surpassing the Teacher in One Step.\" arXiv preprint arXiv:2410.14919 (2024).\n\n[6] Tian, Keyu, et al. \"Visual autoregressive modeling: Scalable image generation via next-scale prediction.\" Advances in neural information processing systems 37 (2024): 84839-84865.\n\nQUESTIONS:\nBesides the weaknesses above, the authors need to thoroughly discuss this work's relation to previous works because I feel the paper does not pay proper attention to prior methods and the originality is a bit oversold.\n\nLIMITATIONS:\nThere are no direct negative societal impacts, although such technologies wider ethical implications can be discussed more.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 5, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents MeanFlow, a novel one-step generative modeling framework. It introduces the concept of average velocity to characterize flow fields, contrasting with the instantaneous velocity modeled by traditional Flow Matching methods. By deriving a well-defined relationship between average and instantaneous velocities, the authors establish a theoretical foundation for training neural networks to model the average velocity field. MeanFlow achieves impressive empirical results outperforming previous state-of-the-art one-step diffusion/flow models and narrowing the gap between one-step and multi-step models.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths:\n1. The introduction of the average velocity concept and the derivation of the MeanFlow Identity offer a new perspective and theoretical foundation for one-step generative modeling.\n2. The model can be trained from scratch without relying on pre-training, distillation, or curriculum learning, simplifying the training process.\n3. Experimental results indicate that MeanFlow models scale well with increasing model size and training duration, suggesting potential for further performance improvements.\n4. The paper provides thorough theoretical analysis and derivation, supporting the validity and effectiveness of the proposed method.\n### Weaknesses:\n1. Compared to Flow Matching, MeanFlow incurs additional training time due to the computation of the Jacobian-vector product, which might be a limitation in resource-constrained settings.\n2. The paper focuses on generation quality but lacks in-depth analysis and discussion on the diversity of the generated samples.\n\nQUESTIONS:\n1. The paper mentions that MeanFlow incurs additional training time due to the computation of the JVP, even with the use of stop-gradient. Could the authors provide a detailed comparison of the training time between MeanFlow and other methods? \n2. The paper primarily focuses on the quality of generated samples using metrics like FID but does not provide an in-depth analysis of the diversity of the generated samples. Could the authors report additional metrics that assess the diversity of the generated samples, such as the Inception Score (IS)? This would provide a more comprehensive evaluation of MeanFlow's performance in terms of both quality and diversity, giving a clearer picture of its capabilities and limitations.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a novel training objective to improve one-step generation in the flow matching framework. The core idea is to define the average velocity u as the integral of marginal velocity v over a segment (r, t), and to express u in terms of v and du/dt, which leads to a new loss formulation. The method enables one-step generation with a single, unified model trained from scratch—without requiring curriculum learning or distillation. The approach achieves state-of-the-art FID scores on ImageNet 256×256.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n1. The proposed method is simple yet effective.\n2. The performance is strong and competitive.\n3. The method is scalable in terms of both model size and image resolution.\n4.  The paper is well-written and easy to follow.\n5.  Compared to distillation-based approaches, the method avoids many heuristic components \n6.  It naturally supports classifier-free guidance (CFG), enhancing its applicability in conditional generation.\n\n## Minor Weaknesses\n- The method cannot be used with classifier-free guidance (CFG) sampling. (If this is incorrect, please clarify.)\n\nQUESTIONS:\n## Questions\n1. Could the authors elaborate on the training stability of the model and compare it with the consistency models? For example, does it consistently converge under different random initializations? Is it particularly sensitive to certain hyperparameters, such as the batch size?\n2. Given that the proposed training objective involves additional terms, how much slower is the training process compared to standard flow matching when aiming for comparable FID?\n3. In Figure 2 and Equation (6), average velocity is described as the marginal velocity minus its derivative. However, in practice, v is defined as e - x (i.e., conditional flow matching velocity). Could the authors provide more theoretical or intuitive justification for why this formulation remains stable during training?\n4. The use of Jacobian-vector products (JVPs) seems potentially memory-intensive. I wonder whether this could pose a scalability bottleneck, especially as the data or model dimensionality increases. Could the authors discuss how this affects scalability in practice, and whether any memory optimizations or approximations were considered?\n5. In the ablation study, the reported FID scores appear significantly higher than the main results. Why?\n\nLIMITATIONS:\nThe limitations of the work are reflected in the identified weaknesses and the questions posed.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes MeanFlow, a one-step generative modeling framework built on the concept of an average velocity field in diffusion/flow-based generative models. Instead of modeling the instantaneous velocity as in standard Flow Matching, the authors define an average velocity. To do this, the authors derive a fundamental “MeanFlow Identity” which provides a principled training objective for a neural network to approximate the true average velocity field without needing to explicitly compute any time integrals during training.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n- Novel Theoretical Contribution: The introduction of average velocity fields and the MeanFlow Identity is a clear conceptual innovation. It provides a new theoretical lens on one-step generation. Importantly, this framework generalizes and unifies prior ideas. For example, it inherently enforces trajectory consistency (one big step vs. multiple small steps) as a property of the ground-truth field, instead of imposing consistency as an external loss.\n\n- MeanFlow does not rely on distilling a pre-trained multi-step model. This makes the approach conceptually cleaner and potentially easier to reproduce. This principled foundation likely contributes to stable and robust training. The authors report that no special tricks beyond the derived loss were required.\n\n- The paper demonstrates impressive results for one-step generative models. These results are obtained from scratch (no pre-trained models) and using a consistent architecture for fair comparison. The experiments cover both high-resolution image generation (ImageNet 256) and low-resolution CIFAR-10, showing that MeanFlow scales across datasets.\n\n- Impact and Relevance: This work is timely and impactful for the generative modeling community. Closing the gap to multi-step diffusion with a one-step model is a longstanding challenge – it has direct implications for faster generative model deployment and could spur new research into flow-based modeling.\n\n**Weaknesses**\n- Theoretical rigor: In standard flow-matching frameworks, the gradients of the flow matching loss and conditional matching loss have been rigorously shown to be equivalent. However, it remains unclear whether such equivalence also holds for the formulations proposed in this paper (Eqs. 9, 10, and 11). Although empirical results indicate strong performance, the theoretical correctness and justification of these equations are not fully established. Clarifying this point would significantly strengthen the theoretical grounding of the method.\n\n- Limited evaluate metric: The performance is currently evaluated exclusively using FID scores, which limits the understanding of the method’s quality along other important dimensions such as sample diversity, mode coverage.\n\nQUESTIONS:\n- Could the authors provide more detailed comparisons regarding the training complexity and computational cost relative to existing one-step baseline methods? While FLOPs and timing details are briefly presented in Table 4 and Appendix B.4, a direct and explicit comparison to baseline methods would further clarify practical feasibility and advantages.\n\n- Could the authors report performance using other generative metrics such as Inception Score, sFID, Precision, and Recall? These metrics would offer deeper insights into aspects like diversity, mode coverage, and overall perceptual quality of generated samples. Additionally, evaluating the method with FID-DINO may provide a more accurate assessment of semantic fidelity and visual realism.\n\n- As mentioned in the weaknesses, could the authors clarify whether substituting Eq. 11 into Eq. 10 maintains theoretical equivalence?\n\nLIMITATIONS:\nThere is no explicit limitation or potential societal impact mentioned in the paper.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces \"MeanFlow,\" a novel framework for one-step generative modeling. \nThe core idea is to move away from modeling the instantaneous velocity, as in Flow Matching, and instead model the average velocity over a time interval. \nThe authors derive a \"MeanFlow Identity\", a differential equation that connects the average velocity to the instantaneous velocity. \nThis identity is then used to construct a training objective that allows a neural network to learn the average velocity field directly, using only the ground-truth instantaneous velocity as a signal. \nThe key benefit is that a single evaluation of the learned average velocity network can approximate the entire flow from noise to data, enabling high-quality 1-NFE (Number of Function Evaluations) generation. \nThe authors demonstrate state-of-the-art results for one-step generation on ImageNet 256x256, significantly outperforming previous methods.\n\nSTRENGTHS AND WEAKNESSES:\n[Strength]\n1. The primary strength of this work is its outstanding performance. An FID of 3.43 with a single function evaluation on ImageNet 256x256 is a remarkable achievement among one-step generative models. The 2-NFE result of 2.20 is also highly competitive, rivaling many-step diffusion models. These results alone make the paper a significant contribution.\n2. The idea of modeling average velocity is intuitive and theoretically clean. The derivation of the \"MeanFlow Identity\" (Eq. 6) from the fundamental definition of an integral appears sound and provides a solid theoretical underpinning for the method.\n3. The proposed model is trained from scratch and does not require pre-trained teacher models, distillation, or the complex \"discretization curriculum\" that some consistency models rely on. This simplifies the training pipeline considerably.\n\n[Weakness]\nNo major flaws are presented in this paper. I only have several suggestions here:\n1. Limitaiton section. The paper presents the MeanFlow model as a flawless solution. However, no method is perfect. The authors explicitly answer NO to the question of discussing limitations in their checklist. This is a significant omission. A thorough scientific paper should discuss potential failure modes.\n2. MeanFlow relies on the instantaneous velocity of flow matching, i.e., v_t = \\epsilon - x. However, is it the best choice?\n\nQUESTIONS:\nN/A\n\nLIMITATIONS:\nN/A", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-07-03"}