Title: Adaptive Inference-Time Scaling via Cyclic Diffusion Search
Venue: NeurIPS 2025
Accepted: yes
Keywords: Diffusion model

Inference-time scaling
Abstract: Diffusion models have demonstrated strong generative capabilities across domains ranging from image synthesis to complex reasoning tasks. However, most inference-time scaling methods rely on fixed denoising schedules, limiting their ability to allocate computation based on instance difficulty or task-specific demands adaptively. We introduce the challenge of adaptive inference-time scaling—dynamically adjusting computational effort during inference—and propose Adaptive Bi-directional Cyclic Diffusion (ABCD), a flexible, search-based inference framework. ABCD refines outputs through bi-directional diffusion cycles while adaptively controlling exploration depth and termination. It comprises three components: Cyclic Diffusion Search, Automatic Exploration-Exploitation Balancing, and Adaptive Thinking Time. Experiments show that ABCD improves performance across diverse tasks while maintaining computational efficiency.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes an idea to use a pre-trained diffusion model to generate $\\arg\\max_x r(x)$ for some black-box reward function $r$. To simultaneously handle exploitation and exploration, they map the initially predicted data into multiple noise levels and re-denoise them in parallel. They also propose a way to adaptively terminate the sampling process.\n\nSTRENGTHS AND WEAKNESSES:\n# Strengths:\n\n- The idea is simple, and the motivation is sound. The concept of performing both exploitation and exploration in a parallel manner is interesting.\n- The topic--learning to optimize test-time reward using a pre-trained generative prior--is timely and of interest to the community.\n\n# Weaknesses:\n\n- Experiments are done on a relatively small scale. However, this is sufficient to analyze the proposed method in a controlled way, so this is not considered a significant weakness in the reviewer's opinion.\n- Always denoising all samples from all $t'$ seems inefficient. This could be made more efficient by selecting $t'$ more intelligently.\n- The adaptive termination criterion could have been compared to a simpler stopping criterion that checks whether the reward has stagnated.\n- In the experimental results, the performance gap between some existing baselines appears moderate. For instance, in Sudoku, SoP performs on par with the proposed method.\n- Comparing wall-clock time does not seem to provide the full picture. See questions.\n\nQUESTIONS:\n- Have the authors tried a simpler adaptive termination method that only checks whether the reward is improving or not? Does the proposed method offer any advantage over this simple baseline? The proposed method terminates when high-reward samples are mostly from small $t'$, but this discards the case where local exploration keeps improving, in which case it may be too early to terminate the algorithm. \n- Intuitively, low $t'$ encourages exploitation, whereas a large $t'$ promotes exploration. Does this mean that in environments where exploration is more important (e.g., when the reward support is far from the pre-trained model's support), BoN will outperform the proposed method? I can imagine that when all initial samples receive very low rewards, adding small noises to them and denoising them again can be a waste of compute. It might be better to just start with fresh samples.\n- As mentioned in the paper, SoP uses a similar back-and-forth denoising->re-noising process. What is the benefit of ABCD over SoP? One disadvantage of SoP (and all other baselines compared) is that it uses $r(\\mathbb{E}[x_0 \\mid x_t])$ as an approximation of the true reward, which is not very reliable--correct? Is there any advantage of SoP over ABCD? A more detailed comparison would be helpful.\n\n\n>For fair comparison, the total number of particles was set equal across all methods (except BoN).\n\nDoes the same number of particles imply the same number of forward passes of the score function? If not, it would be better to report the latter as well, so that readers can clearly compare the computational efficiency in terms of FLOPs.\n\nFor the same reason, wouldn’t it be better to report the number of forward passes instead of “Mean Cyc” in Table 2?\n\nIn Table 1, what does “success” mean? The distance to the goal is not 0. Do you use a threshold value and consider a particle successful when the distance is below that threshold? This part is not clearly explained.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 4, "ORIGINALITY": 2, "DATE": "2025-06-25"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work introduces Adaptive Bi-directional Cyclic Diffusion (ABCD), a novel inference framework for diffusion models that automatically discovers improved denoising trajectories based on a given reward function. The core innovation lies in replacing fixed denoising schedules with a flexible, search-based approach that cycles bidirectionally through the diffusion process. ABCD has three main components: (1) Cyclic Diffusion Search, which alternates between denoising and re-noising steps; (2) Automatic Exploration-Exploitation Balancing, which distributes particles across multiple noise levels; and (3) Adaptive Thinking Time, which provides a stopping criterion. The authors evaluate their method on a range of tasks, including maze navigation, Sudoku solving, molecular generation, and planning, demonstrating improved performance and computational efficiency compared to baselines.\n\nSTRENGTHS AND WEAKNESSES:\n### **Strengths**\n\n* The paper addresses an important limitation in current diffusion model inference—namely, the rigidity of fixed denoising schedules.\n* The bi-directional cycling approach and adaptive termination are novel contributions.\n* The adaptive termination criterion based on the temperature distribution is conceptually interesting.\n* The writing is clear, with effective use of figures, and the method is presented with sufficient detail for reproducibility.\n* The experimental evaluation spans multiple domains, demonstrating consistent improvements.\n* The method is compatible with both differentiable and non-differentiable reward functions.\n\n\n### **Weaknesses**\n\n* The main weakness of the paper is the lack of experiments on more complex, real-world problems such as image generation or language modeling. Including such experiments would significantly strengthen the contribution by demonstrating ABCD’s applicability to practical scenarios. At present, it remains unclear how well the method translates to real-world tasks like text-to-image generation.\n\n* The highest-performing configurations of ABCD still require significantly more inference time than baseline sampling. A more detailed analysis of computational overhead—including how varying the budget allocated to each ABCD component affects final quality—would be helpful for understanding the trade-offs.\n\n* The method’s reliance on DDIM initialization may introduce failure modes that are not fully addressed. An ablation study evaluating the impact of different initialization strategies would help assess the robustness of ABCD.\n\nQUESTIONS:\n- How does ABCD perform when DDIM initialization produces only poor samples? Are there any other possible failure modes?\n\n - Have you tested ABCD on more complex problems (such as small scale image generation)? Even modest increases in performance would provide valuable insights into scalability toward real world applications.\n\n- What time-step schedulers and sampling algorithms (e.g. DDIM, DDPM) were used for each baseline method?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

comments: SUMMARY:
The paper proposes adaptive bidirectional Cyclic Diffusion (ABCD), a search-based inference framework for adaptive inference-time scaling for diffusion models with respect to the available computation budget. The authors identified fixed denoising schedules as a bottleneck for inference time scaling, and proposed a renoising and denoising schedule. Experiment results show good performance on a variety of tasks including Sudoku, Pixel Maze, Molecule Generation and OGBench Point Maze

STRENGTHS AND WEAKNESSES:
(+) the idea of Adaptive Inference-Time Scaling and the ABCD frame, to my knowledge, is novel and good first explorations to this direction and can inspire future work

(+) Experiments were conducted in a comprehensive set of tasks including Sudoku, Pixel Maze, Molecule Generation and OGBench Point Maze and all show promising results

(+) ablations seems good to me 

(-) The experiments and proposed method are mostly experimental instead of theoretical. Not much theoretical justification

QUESTIONS:
Would the method work well for tasks such as text-to-image or text-to-video that diffusion models are widely applied to?

LIMITATIONS:
n/a
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-02

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper tackles the problem of inference-time optimization in diffusion models when a predefined reward function is available. The authors propose Adaptive Bi-directional Cyclic Diffusion (ABCD), a search-based inference framework composed of three main steps.\nFirst is the Cyclic Diffusion Search: $N$ particles are denoised from pure Gaussian noise, evaluated using the reward function, and the top-$K$ are selected. These are then re-noised, and the denoise-rank-renoise cycle is repeated. To adaptively balance exploration and exploitation, the method re-noises to multiple noise levels rather than a fixed one, with higher noise levels corresponding to more exploratory search and the lower noise levels corresponding to local refinement. The cycle terminates once all top-$K$ samples are obtained from low renoised samples, indicating local convergence.\nThe authors evaluate ABCD on several reasoning and planning tasks, including Sudoku and maze solving, showing impressive  improvements over previous methods.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n* The paper is very well written and easy to follow. \n* The proposed approach is simple, intuitive, and quite elegant. \n* The experimental improvements are impressive, with the proposed approach improving on both speed and quality (success rate). \n\n**Weaknesses:**\nThe paper is an extremely good one, and the following weaknesses are more nitpicks rather than actual weaknesses. \n* All experiments are done on relatively low-dimensional data. As pointed out by the authors, it remains unclear how well the approach would scale to high-dimensional outputs, such as high-resolution text-to-image generation. \n* One of the main concepts of the paper is using multiple noise levels during the renoising step, discussed in 3.2. However, denoising higher noise levels requires more function evaluations of the base model than lower noise levels. As a result, during the end of the search process, where only local refinement is needed, some amount of unnecessary compute is being performed by distributing each sample uniformly along the $M$ noise levels.\n\nQUESTIONS:\n* How many denoising steps are used at each of the noise levels $\\{t_1, t_2, \\dots, t_M\\}$? Is this a constant fixed amount or does it change based on the noise level?\n* Does the algorithm utilize any form of \"history\" to save the best top-K during the different cycles? This question mainly comes from the fact that the curves in Figures 6,7 are not always increasing w.r.t. the inference time which seems counter-intuitive.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}