Title: Greed is Good: A Unifying Perspective on Guided Generation
Venue: NeurIPS 2025
Accepted: yes
Keywords: Flow matching

diffusion models

neural differential equations

guided generation

numerical methods

dynamical systems
Abstract: Training-free guided generation is a widely used and powerful technique that allows the end user to exert further control over the generative process of flow/diffusion models.
Generally speaking, two families of techniques have emerged for solving this problem for *gradient-based guidance*: namely, *posterior guidance* (*i.e.*, guidance via projecting the current sample to the target distribution via the target prediction model) and *end-to-end guidance* (*i.e.*, guidance by performing backpropagation throughout the entire ODE solve).
    In this work, we show that these two seemingly separate families can actually be *unified* by looking at posterior guidance as a *greedy strategy* of *end-to-end guidance*.
    We explore the theoretical connections between these two families and provide an in-depth theoretical of these two techniques relative to the *continuous ideal gradients*.
    Motivated by this analysis we then show a method for *interpolating* between these two families enabling a trade-off between compute and accuracy of the guidance gradients.
We then validate this work on several inverse image problems and property-guided molecular generation.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper shows that posterior guidance is a greedy approximation of end-to-end guidance, and presents a unifying framework for training-free guided generation in flow/diffusion models. The authors derive error bounds (Theorems 5.4, 6.1) linking greedy and exact gradients, and propose higher-order solver to trade off compute vs. accuracy. Experiments on inverse imaging and molecule generation control illustrate the performance of new insight.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n1. First to cast posterior guidance as a greedy end-to-end approximation under certain assumptions.\n2. Rigorous theoretical analysis with clear theorems on greedy vs. full gradients and then derive error bounds (Theorems 5.4, 6.1).\n\nWeaknesses\n1. Results rely on affine paths and smoothness assumptions. Real-world flow/diffusion models often include non-affine terms or non-Gaussian noise, so it’s unclear whether the proofs can extend to more complex settings.\n2. Experiments are only proof of concept and do not demonstrate clear practical superiority.Limited empirical evidence of real-world benefit and underperform SOTA.For example, in Table 1 Greedy (2-step Euler) falls behind DAPS(B. Zhang et al. 2024) by only a narrow margin, whereas the basic Greedy algorithm performs significantly worse than D-flow(Ben-Hamu et al.2024).\n3. Experimental illustrations are limited,offers error bounds but no empirical runtime vs. quality trade-off Figures to guide method selection.The experimental evaluation lacks sufficient task diversity, omitting important scenarios such as editing and conditional generation.\n\nReferences\nBen-Hamu, H., Puny, O., Gat, I., Karrer, B., Singer, U., and Lipman, Y. (2024). “D-Flow: Differentiating through Flows for Controlled Generation.” Proceedings of the 41st International Conference on Machine Learning. URL: https://openreview.net/forum?id=SE20BFqj6J (cit. on pp. 1–3, 6, 8, 9, 17–19, 21, 22, 24, 33, 34)\nZhang, B., Chu, W., Berner, J., Meng, C., Anandkumar, A., and Song, Y. (2024). “Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing.” arXiv preprint arXiv:2407.01521 [cs.LG]. URL: https://arxiv.org/abs/2407.01521 (cit. on pp. 7, 8, 17, 32–35)\n\nQUESTIONS:\n1.Failure Analysis: The greedy method fails badly for some molecule generation. Please analyze why (e.g. non-convexity, learning-rate issues).\n\n2. Baseline Comparison: Explicitly compare to similar recent works(“greedy (midpoint)” v.s. midpoint guidance (Moufad et al., 2025)) to better position your hybrids.\n\nReferences\nMoufad, B., Janati, Y., Bedin, L., Durmus, A. O., Douc, R., Moulines, E., and Olsson, J. (2025). “Variational Diffusion Posterior Sampling with Midpoint Guidance.” Proceedings of the 13th International Conference on Learning Representations. URL: https://openreview.net/forum?id=6EUtjXAvmj (cit. on pp. 17, 18, 32, 34, 42)\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 2, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper provides a unifying theoretical framework for two seemingly distinct families of training-free guided generation techniques used in flow and diffusion models: posterior guidance and end-to-end guidance. Both techniques control the generative process, often by injecting gradients from a target prediction model to steer the generation towards desired properties. The authors analyze both approaches and show that posterior guidance can be framed as a greedy gradient step within the end-to-end scheme.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n- Theoretical Unification: The paper's primary strength lies in the theoretical framework that unifies posterior guidance and end-to-end guidance. This provides a deeper understanding of their relationship and is a significant conceptual contribution to the field of guided generation.\n\n**Weaknesses**\n\n- Experiments:  \n  - While the authors show results of experiments for 3 variants in the interpolation space (Euler, midpoint, 2-Euler), I find the experimental setup lacking. Given the theoretical connection that were drawn between the posterior guidance approach and the end-to-end approach, a more elaborate ablation on the various interpolation intermediate steps between the two would greatly improve the understanding of the practical implications of the theoretical findings. Do the experimental results behave as one would expect? Is there anything surprising, as many theoretical results do not transfer to practice in high dimensional regims, and with neural networks.   \n  - One of the claims is that this interpolation allows to trade quality and efficiency, it is not clearly demonstrated in the paper.    \n- It would be valuable to better position this paper in existing literature, see e.g., [\\[2410.00083\\] A Survey on Diffusion Models for Inverse Problems](https://arxiv.org/abs/2410.00083) \n- Clarity: it is hard to parse what the different methods are, adding algorithm boxes with pseudo code would improve ease of understanding.\n\nQUESTIONS:\n- Some reference to prominent approaches are missing. Can the authors explain the connections between the analysed methods and e.g., \\[1\\] and \\[2\\]?\n\n\\[1\\] [\\[2311.16424\\] Manifold Preserving Guided Diffusion](https://arxiv.org/abs/2311.16424)\n\n\\[2\\] [Pseudoinverse-Guided Diffusion Models for Inverse Problems](https://openreview.net/forum?id=9_gsMA8MRKQ)\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors explore the theoretical connections between these two families and provide an in-depth theoretical understanding of these two techniques relative to the continuous ideal gradients. Motivated by this analysis, they then show a method for interpolating between these two families enabling a trade-off between compute and accuracy of the guidance gradients. they validate this work on some inverse image problems and property-guided molecular generation.\n\nSTRENGTHS AND WEAKNESSES:\n### Strength\n\n1. The theoretical part of the paper is structured clearly and presented in a concise and readable manner.\n2. The paper presents substantial theoretical analysis on posterior guidance and end-to-end optimization, which could potentially inspire future advances in method design.\n\n### Weakness\n\n1. Including more illustrations and pseudocode would help readers better understand the overall workflow of the paper and how the proposed theoretical insights lead to concrete improvements.\n2. While training-free guidance methods are known to face substantial limitations—including limited controllability, off-manifold generation, longer sampling requirements, and sensitivity to hyper-parameters—the paper does not provide further analysis or exploration toward addressing these challenges, which could have strengthened the contribution.\n3. While the paper outlines future directions involving more hyperparameters and case-specific design choices, it is worth noting that training-free methods are already known to be highly sensitive to hyperparameters, which raises concerns regarding the feasibility and robustness of such approaches.\n\nQUESTIONS:\n1. How the theoretical analysis close the gap between practice and theory? The experimental results leave room for improvement.\n2. Could more state-of-the-art methods be unified under the proposed framework to better demonstrate its practical relevance? Additionally, how does the framework concretely indicate potential directions for future advancements?\n\nLIMITATIONS:\nYes, the authors have discussed the limitations and future work in the Appendix", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents a novel and elegant theoretical framework that unifies two major families of training-free guided generation: posterior guidance (e.g., DPS) and end-to-end guidance (e.g., D-Flow). The central contribution is the formal demonstration that posterior guidance can be viewed as a \"greedy,\" first-order Euler approximation of the more computationally expensive end-to-end guidance.\n\nThe authors provide a rigorous mathematical analysis to support this claim, showing the equivalence of the posterior guidance gradient to a single explicit Euler step in a DTO scheme and to the first iteration of a fixed-point method for an implicit Euler discretization in an OTD scheme. Furthermore, the paper provides a formal error analysis bounding the difference between the \"greedy\" gradient and the \"true\" gradient from end-to-end backpropagation.\n\nBuilding on this unified view, the authors propose a framework, suggesting that higher-order numerical solvers can be used to interpolate between the two guidance families, offering a potential trade-off between computational cost and gradient accuracy.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\nTo the best of my knowldege, the unification of posterior and end-to-end guidance is novel. The \"greedy\" perspective is intuitive, and likely to have a good view of the field. The theoretical claims seem valid and are supported by the proofs in the appendix (I didnt fully validated the proofs). Lastly, the proposed framework is a native extenstion of the theory. \n\n**Weaknesses**\n\n* Explore more solvers: I wonder how the results will look like with higher-order solvers. Does the trend being maintined? \n* Limited scope of experiments: I think that the experiments can benefit from a deeper analysis of task complexity vs. method being used. \n* Limitations: I couldnt find any refernfce to limitation of the work. \n\nI believe the theoretical contribution of this paper is strong and the community will benefit from this work.\n\nQUESTIONS:\nStabilty of results: In Table 2, the euler results, seem very unstable, can the authors confirm that this is true and not originated from some bug?\n\nLIMITATIONS:\ni dont believe there are potential negative societal impact", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}