Title: Inference-Time Scaling for Flow Models via Stochastic Generation and Rollover Budget Forcing
Venue: NeurIPS 2025
Accepted: yes
Keywords: Inference-time scaling

flow model

reward alignment
Abstract: We propose an inference-time scaling approach for pretrained flow models. Recently, inference-time scaling has gained significant attention in LLMs and diffusion models, improving sample quality or better aligning outputs with user preferences by leveraging additional computation. For diffusion models, particle sampling has allowed more efficient scaling due to the stochasticity at intermediate denoising steps. On the contrary, while flow models have gained popularity as an alternative to diffusion models--offering faster generation and high-quality outputs--efficient inference-time scaling methods used for diffusion models cannot be directly applied due to their deterministic generative process. To enable efficient inference-time scaling for flow models, we propose three key ideas: 1) SDE-based generation, enabling particle sampling in flow models, 2) Interpolant conversion, broadening the search space and enhancing sample diversity, and 3) Rollover Budget Forcing (RBF), an adaptive allocation of computational resources across timesteps to maximize budget utilization. Our experiments show that SDE-based generation and variance-preserving (VP) interpolant-based generation, improves the performance of particle sampling methods for inference-time scaling in flow models. Additionally, we demonstrate that RBF with VP-SDE achieves the best performance, outperforming all previous inference-time scaling approaches.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes a new method for inference-time scaling in pretrained flow models, making them competitive with diffusion models for tasks requiring reward alignment (e.g., compositional or quantity-aware image generation). The key contributions are:  introducing SDE-based stochasticity into flow models for effective particle sampling, interpolant conversion (linear to variance-preserving) to broaden the search space/diversity, and Rollover Budget Forcing (RBF) for adaptive allocation of computational budgets during inference.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**:\n\n- Includes diverse test cases, comparisons to multiple baselines, and ablation on key techniques (SDE, interpolant conversion, RBF).\n- Outperforms prior inference-time scaling baselines on compositional and quantity-aware image generation tasks. Demonstrates both quantitative and qualitative improvements.\n- Clear and easy-to-follow presentation.\n\n**Weaknesses**: \n\n- It is ambiguous why authors choose this setup heuristically: “In our case, we set $g(t) = t^2$, scaled by a factor of 3.”\n- After all the transformations, the paper finally uses the VP-SDE. I questioned the novelty of the paper. It appears that all transformations can be eliminated by utilizing direct paths in the VP-SDE diffusion model. This point should be discussed, or at least an experiment around this selection should be included.\n- Some papers show that the denoising steps of flow models should not be uniform [1], [2]. A comparison between your time schedule design in Appendix D and the time schedule in these papers is recommended.\n- The paper introduces methods that add computational cost at inference. There’s limited discussion or quantitative analysis of this trade-off.\n- The paper consists of several modules that are built upon each other. However, the paper lacks some ablation studies on them and important hyperparameters.\n\nQUESTIONS:\n- In Section 5, the authors suggest that an uneven allocation may be more effective than a uniform one. This idea has been previously explored in several works on flow models [1], [2] and diffusion models [3]. In particular, [2] shows that the trajectory of flow models tends to be more curved at the beginning and end of the denoising process, implying that more NFEs should be allocated to these stages. Does this observation support the design presented in Appendix D, or does it contradict it? \n\n- From my perspective, the inference time scaling for the diffusion model is especially valuable in tasks such as molecular generation where the runtime does not matter. It would be great to see how this work is applied to this domain.\n\nLIMITATIONS:\nyes\n\n**References**\n\n[1] Shaul, N., Perez, J., Chen, R. T., Thabet, A., Pumarola, A., & Lipman, Y. (2023). Bespoke solvers for generative flow models. arXiv preprint arXiv:2310.19075.\n\n[2] Bao Nguyen, Binh Nguyen, and Viet Anh Nguyen. \"Bellman Optimal Step-size Straightening of Flow-Matching Models.\" arXiv preprint arXiv:2312.16414 (2023).\n\n[3] Lu, Cheng, et al. \"Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps.\" Advances in Neural Information Processing Systems 35 (2022).", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-11"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper considers inference time scaling for generating high quality images using flow models by leveraging the existing inference time scaling methods. The paper proposes three techniques to achieve the above purpose, which are (1) extending the deterministic ODE sampling to stochastic sampling, (2) transforming the stochastic sampling to VP-based stochastic sampling, and (3) Rollover Budget Forcing to dynamically allocate the computational resources over timesteps.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: \n(1) The main contribution of the paper is to convert the deterministic ODE sampling of flow models to VP-based stochastic sampling to be able to use existing inference time scaling methods developed for diffusion models. \n(2) Extensive experimental results confirms the effectiveness of the proposed techniques.   \n\nWeaknesses: \n(1) As noted in the paper, the processes for convert the deterministic ODE sampling of flow models to stochastic sampling is already covered in the SiT [38]. Even though the SiT paper focus on improving sampling quality of flow models, the mathematical derivations for converting deterministic sampling of flow models to stochastic sampling are well explained. This makes Subsection 4.3 on Inference-Time SDE Conversion prior work instead of new contribution.  \n\n(2)  It is also known from literature [33] and [52] how to convert a stochastic sampling to a VP-based stochastic sampling.   I would suggest the authors to rewrite Subsection 4.3 on Inference-Time Interpolant Conversion in order to better explain why the conversion makes the search space larger.  In the paper, the authors simply state that \"In Fig.3(c), we visualize the sample diversity under VP-SDE using FLUX which generates more diverse samples than Linear-SDE.\" My question is what the reason behind it. Can the authors provide some intuitive argument?\n\nQUESTIONS:\nSee my comments above.\n\nLIMITATIONS:\nThe authors mentioned that their method introduces additional inference-time overhead. But it is not clear how much additional overhead is introduced by the method.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-25"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces VP‑SDE, an inference‑time scaling framework for pretrained flow models that brings the benefits of particle sampling—previously exploited in diffusion models—to the deterministic flow setting. First, it casts flow generation as an SDE, enabling Monte Carlo sampling of multiple trajectories. Second, it enlarges the candidate output space via a Variance‑Preserving (VP) interpolant conversion. Third, it allocates computational budget adaptively across timesteps through Rollover Budget Forcing (RBF), dynamically adjusting the number of function evaluations (NFEs). Empirical results on Compositional Text‑to‑Image Generation and Quantity‑Aware Image Generation demonstrate that VP‑SDE with RBF outperforms prior inference‑time scaling methods for flow and diffusion models.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n\n- The paper pioneers the integration of particle sampling into flow matching models by reformulating the deterministic probability path evolution as a stochastic process, achieving a more effective exploration–exploitation trade‑off.\n\n-  The manuscript is well organized and reads smoothly; theoretical derivations are detailed and easy to follow.\n\n-  The supplementary material is thorough and supports the main text with additional proofs and experimental details.\n\n## Weaknesses\n\n-  Prior works (e.g., SiT) have already applied very similar techniques to improve the sampling process; this paper adopts those ideas almost unchanged, resulting in limited novelty.\n\n-  While the authors claim that stochastic, variance‑preserving sampling strategies help discover high‑reward, low‑density regions, they provide neither rigorous theoretical justification nor dedicated ablation studies to substantiate this claim, leaving the exploration benefit insufficiently supported.\n\nQUESTIONS:\n1. Can you provide a detailed time‑ and space‑complexity analysis of each sampling strategy (e.g. vanilla flow, SDE‑based, VP interpolant, RBF) under a fixed compute budget? In particular, is Rollover Budget Forcing (RBF) truly optimal in all regimes, or only once you scale up the model?\n\n2. The phrase “much clearer posterior mean” on line 241 is vague—what metric or visualization supports this description?\n\n3. Could you supply a comprehensive list of all critical hyperparameters (e.g. number of particles, RBF schedule parameters, step size for SDE integration) and the rationale behind their chosen values?\n\n4. How sensitive are your results to the number of particles and the specific RBF allocation schedule?\n\n5. Have you tested VP‑SDE and RBF on other flow model variants (e.g. neural ODE flows, continuous normalizing flows) or non‑image tasks (e.g. audio, tabular data)?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper adapts particle sampling to flow-matching models. Particle sampling consists of generating several candidates along the denoising process and picking the best according to a defined reward function. Flow-matching models are deterministic, and thus cannot generate several candidates to enable particle sampling. To address this, the paper proposes two changes to the sampling process of flow-matching models: it derives the stochastic path corresponding to the flow-matching ODE (this introduces the stochasticity needed to generate several candidates) and converts the uniform interpolant to the VP interpolant commonly used in diffusion models (this increases the variance of the generated candidates). On top of these changes, the authors propose a greedy budget-allocation strategy that greedily distributes the number of particles generated at each denoising time-step. These 3 changes are evaluated and perform well on compositional text-to-image generation and quantity-aware generation.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n- The paper is very well written and builds up its ideas in a clear and understandable manner. Synthetic examples provide good illustrations.\n- The proposed ideas, namely VP-SDE sampling of flow models performs well, compared to the baseline, non-stochastic or linear variants, in some cases.\n\n## Weaknesses\n1. The comparison with diffusion models needs more discussion: the authors effectively propose a method diffusion-ify a pre-trained flow model. The comparisons should be between a particle sampling method applied to diffusion models vs the authors' VP-SDE flow models. The authors provide a table in the appendix comparing base diffusion and base flow models but the more interesting comparison is one where both are using particle-sampling. Does the NFE advantage of flow models persist in that setting as well? Is the paper's message that if one wants to do inference-time scaling, then convert the flow-model to a diffusion model at inference time? Moreover, some care is necessary when comparing more recent, larger flow models with older diffusion models.\n2. The two main ingredients of the paper which are:  1)changing between deterministic ODEs and stochastic paths and 2) interpolant conversion of a pre-trained model are known results. The combination and the end-goals are different, which is why I still recommend acceptance. However, the method is not adapting particle sampling to flow-models, but rather making flow-models as diffusion model like as possible to apply existing inference time-scaling methods.\n---\nminor point: The Laplacian symbol $\\Delta$ might be better to avoid confusion with the Hessian symbol in the proof of Proposition 1.\n\nQUESTIONS:\n1. The greedy budget re-allocation scheme is interesting. However, from Figure 9, it seems that it is \"rare\" for the `time of occurrence of higher reward` to exceed the uniform budget. If the authors were to remove the budget reallocation strategy but simply cut the uniform budget early (i.e removing line 7 in alg.2) does RBF simply become CODE? Please correct my understanding if not. Moreover, it appears that RBF is harder to parallelize compared with other search schemes. Could the authors discuss this some more?\n\nLIMITATIONS:\nA limitation the authors should discuss is the aesthetics score, which appears to be harmed by most of the inference time modifications.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-20"}