{"id":"f25d5a91-302e-49f2-aff9-4d82ad8eca5c","arxiv_id":"2508.12361","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A funnel-shaped particle schedule and an adaptive temperature schedule improve SMC-based inference-time scaling for text-to-image diffusion models at fixed compute.","lead":"This paper proposes two simple fixes to inference-time scaling for text-to-image diffusion models: reduce the number of particles as generation progresses, and down-weight unreliable early-stage reward scores. The authors show these tweaks improve image-text alignment (GenEval, ImageReward) on several Stable Diffusion models at the same compute budget.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Funnel-schedule NFE accounting is unverifiable: no stated mapping of [12,10,6,4,4] onto the 30 denoising steps yields the claimed 240 NFE, so the fixed-budget claim at the heart of the paper is not yet auditable.","rationale":"The paper's contribution is conditional on budget-fair comparison: the abstract and Section 5.2 both emphasize 'without increasing the total number of Noise Function Evaluations.' The reader's weakest assumption identifies exactly the missing operational definition: how [12,10,6,4,4] maps onto the 30 denoising steps and why the total remains 240. My own calculation of the natural readings gives 216 or 200, not 240, so this is not a minor exposition gap but a load-bearing reproducibility issue. If the schedule uses more NFE, the empirical improvements are confounded with extra compute; if it uses fewer, the baseline comparison is still undefined. Secondary issues such as the hand-wavy convergence theorem and the HPSv2 discrepancy with the abstract are real but less decisive, because the empirical claim could stand even if the theory is only a citation to standard adaptive-SMC results and the abstract overgeneralizes. The correct disposition is to keep the reader's CONDITIONAL verdict: the concern is concrete and checkable, and the authors can address it with a per-step accounting table or code, so rejection is not warranted on the current evidence, but acceptance is not warranted until the NFE accounting is verified.","tokens_in":14389,"tokens_out":7125,"duration_ms":72270,"concrete_test":"Ask the authors to release, or to specify in text, the exact per-timestep particle count N_t for t=30,...,1 implied by the funnel schedule [12,10,6,4,4], and compute the total NFE as sum_{t=1}^{30} N_t. Verify that this sum equals 240 and that the Best-of-N baseline is charged exactly one NFE per particle per step. If no consistent mapping yields 240, or if the baseline accounting differs, rerun Table 2 with strictly matched NFE and check whether F-SMC-A(D)'s advantage on ImageReward and GenEval persists.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 5.2 states that all methods use a total NFE of 240, equates this with 8 particles for 30 steps, and then asserts that the funnel schedule [12,10,6,4,4] 'maintains the same total NFE.' The manuscript never specifies which particle count is active on which of the 30 denoising steps. Natural readings do not sum to 240: if each of the five entries covers a 6-step block, total NFE is 6*(12+10+6+4+4)=216; if the last block runs from step 10 to step 0 (10 steps), total NFE is 12*5+10*5+6*5+4*5+4*10=200. Appendix A.4 lists candidate schedules and resampling steps but does not give the per-step mapping. Without that mapping, the central claim that F-SMC-A(D) outperforms baselines at fixed compute cannot be checked. If the funnel schedule actually performs more than 240 network evaluations, the reported improvements on ImageReward and GenEval could be explained by additional compute rather than by the method, which would invalidate the headline result. This is a missing invariant in the experimental protocol, not a disagreement about which reward model is preferable.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes two modifications to SMC-based inference-time scaling for text-to-image diffusion models. F-SMC uses a funnel-shaped particle-count schedule that reduces the number of maintained particles as denoising progresses, while SMC-A introduces a time-dependent temperature parameter that linearly increases the influence of early-stage rewards. Combining both, F-SMC-A is claimed to outperform best-of-N, SVDD, and prior SMC baselines on ImageReward and GenEval across SD1.5, SD2.0, SD2.1, and SDXL at a fixed NFE of 240. The authors also present a convergence theorem (Theorem 2) claiming that F-SMC-A converges to the reward-tilted distribution.","tokens_in":14618,"tokens_out":5333,"duration_ms":53112,"significance":"If the fixed-NFE claim holds, the contribution is practically valuable: it improves image-text alignment without increasing inference compute, and the two mechanisms are simple, model-agnostic, and well motivated by the empirical analyses of early-stage reward unreliability and late-stage loss of plasticity. The unified search framework in Table 1 is a useful organizing device, and the decision to tune the funnel schedule on DrawBench and then evaluate on the held-out GenEval benchmark is a methodological strength. The convergence result, however, is essentially a restatement of standard SMC theory and is not a major theoretical advance. The central empirical claim currently rests on an unverifiable NFE accounting and on single-run point estimates without uncertainty quantification.","major_comments":[{"comment":"The fixed-NFE claim is unverifiable as written. The text states that the funnel schedule [12, 10, 6, 4, 4] 'maintains the same total NFE' as 8 particles for 30 steps (240), but it never specifies how the five schedule entries map onto the 30 denoising steps. If the five entries cover five blocks of 6 steps each, the total is 6*(12+10+6+4+4)=216; if the last block covers 10 steps, the total is 12*5+10*5+6*5+4*5+4*10=200. Neither equals 240. Appendix A.4 lists candidate schedules and resampling steps but still does not give the per-step particle counts. Please provide the explicit mapping from denoising step to particle count, and verify the NFE of every baseline and proposed method. If the funnel schedule in fact uses more than 240 network evaluations, the reported gains on ImageReward and GenEval would be attributable to additional compute rather than to the method, invalidating the headline result.","section":"Section 5.2 and Appendix A.4"},{"comment":"The reported results are single-run point estimates with no error bars, repeated seeds, or significance tests. For example, on SD1.5 the GenEval difference between Best-of-N (56.24) and F-SMC-A(D) (57.32) is about one point, and on SD2.0 the difference between SMC(M) (61.12) and F-SMC-A(M) (60.76) is negative; without repeated trials it is impossible to assess whether these differences are meaningful. The central claim that F-SMC-A 'consistently outperforms' all baselines therefore lacks statistical support. Please report means and standard deviations over at least three independent runs (or a clearly justified fixed-seed protocol), and state whether the GenEval and ImageReward evaluations are deterministic given the seed.","section":"Section 5.2, Table 2"},{"comment":"The convergence theorem as stated is not actually proven in the manuscript. The proof establishes that the telescoping product of potentials equals exp(lambda * r(x0, c)) (Eq. 14), which is the target-condition identity by construction, but the convergence of the particle system under time-varying particle counts and time-varying temperature is delegated to Beskos et al. without verifying their sufficient conditions. In particular, the manuscript does not show that the boundedness and smoothness conditions on Gt hold uniformly in t as lambda_t varies, and the relation of the condition N0/Nt > 0 to the Beskos conditions is not explained. Moreover, Appendix A.5 describes the schedule as 'non-increasing' while Section 4.2 defines N_{t-1} < N_t, which is increasing in t; this inconsistency needs to be resolved. Either provide a complete proof sketch that checks the Beskos conditions, or clearly state that Theorem 2 is a corollary of standard adaptive SMC theory and give the precise theorem to which it refers.","section":"Theorem 2 and Appendix A.5"}],"minor_comments":[{"comment":"The abstract states that the approach 'outperforms previous baselines' without qualification, but Table 2 shows that HPSv2 scores for F-SMC-A are generally lower than Best-of-N. The main text acknowledges this limitation, so the abstract should be qualified to say 'outperforms on ImageReward and GenEval' to avoid overclaiming.","section":"Abstract and Section 5.2"},{"comment":"The Diff potential entry is malformed: the formula reads 'exp[λ(rt−rt−1)]†' with a superscripted dagger and no closing bracket, and the footnote '†‡ Whent = 0 ort =T' is unclear. Please clean up the notation and define the boundary cases explicitly.","section":"Table 1"},{"comment":"The phrase 'All methods were evaluated at denoising steps {10, 15, 20, 25, 29}' is confusing: it is not clear whether these are the only timesteps at which resampling or scoring occurs, or whether these are evaluation timesteps. Please clarify the experimental protocol, especially how the 30-step Euler Ancestral sampling interacts with these five steps.","section":"Section 5.2"},{"comment":"The scaling analysis in Figure 6 does not specify the NFE values corresponding to the x-axis points, and no error bars are provided. Please state which budgets were used (e.g., what is the baseline '1x' NFE?) and whether the curves are averages over multiple seeds.","section":"Section 5.3 and Figure 6"},{"comment":"No code or URL is provided for the implementation. Please release code and a detailed protocol (prompts, seeds, resampling steps, exact per-step particle counts) to make the fixed-NFE comparison reproducible.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a timely and relevant problem, and the proposed F-SMC-A is simple and plausible. However, the missing per-step mapping of the funnel schedule makes the fixed-NFE claim unauditable, and the lack of error bars undermines the statistical credibility of the central comparison. These issues are fixable within the scope of a revision, but they are load-bearing and must be resolved before acceptance. The convergence theorem is overclaimed and should either be made rigorous or explicitly reduced to known adaptive SMC results."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Xun and colleagues propose two cheap modifications to SMC-based inference-time scaling for diffusion models: a funnel particle-count schedule and a linearly increasing temperature. The empirical sweep across four SD models and several benchmarks is broad, and the paper correctly identifies a real phenomenon — early rewards are unreliable and late resampling is ineffective. The concavity in Figure 5 and the correlation plots in Figures 4/8/9 are useful evidence for that trade-off. Credit where due: the method is simple, the transfer of standard adaptive-SMC heuristics to this setting is sensible, and the convergence proof, while not novel, is a correct restatement of known results (the telescoping product in the Diff potential genuinely satisfies the target condition).\n\nThe soft spots are real. The biggest one is the NFE accounting. Section 5.2 says all methods use 240 NFE (8 particles x 30 steps), then asserts the schedule [12, 10, 6, 4, 4] \"maintains the same total NFE,\" but never specifies which particle count is used on which denoising step. Natural readings of that schedule — five equal blocks of 6 steps, or a longer final block after resampling at steps 10, 15, 20, 25, 29 — sum to 216 or 200, not 240. There may be some unpublished mapping that works, but the paper gives no way to check. Since the headline claim is \"better at the same compute,\" this missing invariant is load-bearing. Without it, the reported ImageReward/GenEval gains could simply reflect extra network evaluations.\n\nOther issues are more moderate. The abstract's \"outperforms previous baselines\" is unqualified, but HPSv2 is actually worse than Best-of-N on three of four models. The funnel schedule and target temperature are hand-tuned on DrawBench and then reported on GenEval; that is a weak form of held-out evaluation, fine for a workshop but under-powered for a strong claim. No error bars, no seeds, no code. The convergence theorem leans on conditions (boundedness, smoothness in the temperature) that are asserted rather than verified, though they are plausible for bounded reward functions. The statement in Section 5.2 that \"all methods lead to a reduction in HPSv2\" is contradicted by their own SD2.1 row.\n\nThe underlying direction is worth taking seriously, but the evidence as presented is not yet auditable. This paper deserves a serious referee — I would not desk-reject it — but the referee should require the exact per-step particle mapping, a verification that the total NFE matches the baselines, and at least one run with multiple seeds or error bars. If the mapping cannot be provided, the fixed-budget claim should be withdrawn or substantially downgraded.","headline":"Plausible and potentially useful incremental method, but the paper's central fixed-NFE claim is unverifiable as written and needs a mandatory mapping before the results can be trusted.","tokens_in":15190,"tokens_out":4228,"would_cite":false,"duration_ms":43125,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that the exploration–exploitation tradeoff in diffusion-model inference-time scaling is best handled by a funnel-shaped particle schedule plus adaptive temperature, and shows this outperforms best-of-N and prior SMC…","keywords":["diffusion models","inference-time scaling","sequential Monte Carlo","exploration vs exploitation","reward-tilted distribution","adaptive temperature","particle filter","text-to-image alignment"],"falsifier":"Recompute the total NFE: with resampling at timesteps $\\{10,15,20,25,29\\}$ and particle counts $[12,10,6,4,4]$ assigned to the intervals between them, the sum over 30 steps must equal 240. If any natural assignment yields a different total, or if no assignment consistent with the paper's text sums to 240, the performance gain is attributable to a larger compute budget rather than the funnel schedule. Alongside this, re-run F-SMC-A(D) against SMC(D) with 8 particles and 30 steps, both at exactly 240 NFE, to confirm the gain persists under a verifiable budget.","tokens_in":14158,"feed_emoji":"🎨","tokens_out":8909,"duration_ms":78590,"temperature":0.7,"pith_summary":"The paper tries to establish that the exploration–exploitation tradeoff in inference-time scaling of diffusion models can be managed by two modifications to Sequential Monte Carlo (SMC) search: a funnel particle schedule that spends more particles early when trajectories are still malleable, and an adaptive temperature that down-weights reward scores from early, unreliable stages. It claims that the combined method, F-SMC-A(D), outperforms prior scaling baselines—including best-of-N and standard SMC—on ImageReward and GenEval across SD1.5, SD2.0, SD2.1, and SDXL, with the total number of noise function evaluations fixed at 240. If correct, this would mean better text-to-image alignment at no extra inference compute, achieved purely by reallocating when the search effort happens rather than by training or changing the reward model. The paper pins the improvement on a structural observation: early-stage samples are hard to score but easy to reshape, while late-stage samples are easy to score but already committed, so search effort should be front-loaded and early rewards should be discounted.","feed_headline":"Funnel schedule beats best-of-N diffusion search on image alignment","feed_subtitle":"Better text-to-image scores with no extra noise function evaluations.","key_machinery":"The machinery is a unified search framework that casts inference-time scaling as selection (resampling), transition (propagation), and scoring (weighting) over a particle population. Within this framework, F-SMC specifies a time-dependent particle schedule $\\{N_t\\}$ with $N_{t-1} < N_t$ (e.g., $[12,10,6,4,4]$ over the resampling steps), and SMC-A specifies a linearly increasing temperature $\\lambda_t = \\frac{T-t}{T}\\lambda$ inside the potential function $G_t = \\exp[\\lambda_t r_t]$. The load-bearing identity is the telescoping product of potentials over time equaling $\\exp(\\lambda r(x_0,c))$, so the particle system provably targets the reward-tilted distribution; systematic resampling and Tweedie denoising estimates ($x_{0|t}$) supply the practical weighting.","core_discovery":"The central claim is that current SMC-based inference-time scaling for diffusion models is limited by a structural dilemma: reward models cannot reliably evaluate early-stage images despite their long-term importance, and once image structure solidifies in later stages, resampling interventions become largely ineffective. The paper proposes F-SMC-A, which combines a funnel-shaped, monotonically decreasing particle count with an adaptive temperature $\\lambda_t = \\frac{T-t}{T}\\lambda$ that linearly increases the influence of reward over the denoising process, and proves that the method still converges to the reward-tilted distribution $p_{\\text{tar}}(x_0,c) \\propto p_{\\text{pre}}(x_0,c)\\exp(\\lambda r(x_0,c))$ as the number of particles grows (under bounded-potential and particle-ratio conditions). Empirically, F-SMC-A(D)—the variant using the difference potential—achieves the highest ImageReward and GenEval scores across four Stable Diffusion models at a fixed NFE of 240, though its HPSv2 scores are generally lower than the Best-of-N baseline, a point the paper attributes to the reward-model generalization gap.","pith_inferences":["If the NFE mapping of $[12,10,6,4,4]$ onto the 30 steps is verified, the funnel-plus-temperature principle likely transfers to other verifiers, but the optimal funnel shape should depend on how reliable the verifier is at early stages; with a reliable early verifier, front-loading would be less beneficial.","The concave resampling-timing curve suggests a finer-grained schedule could do better than the hand-picked $[12,10,6,4,4]$; a testable extension is to learn the particle-count schedule from a validation set, e.g., by hill-climbing on the five interval counts.","The early-stage reward correlation figures suggest that prompt categories with persistently low correlation (like position) may need category-specific temperatures; this is an implication the paper does not pursue.","The HPSv2 deficit suggests ImageReward-guided search overfits its own metric; ensembling multiple reward models in the potential function would be a natural next step to test robustness."],"forward_implications":["At a fixed total NFE of 240, F-SMC-A(D) achieves the best ImageReward and GenEval scores across SD1.5, SD2.0, SD2.1, and SDXL, beating Best-of-N, SVDD, and standard SMC with both Max and Diff potentials.","The two components each help on their own: the funnel schedule alone improves SMC(M) on three of four models, and adaptive temperature alone improves SMC(D) on all four models, so neither contribution is redundant.","Scaling experiments show that F-SMC-A reaches ImageReward levels comparable to or better than Best-of-N while spending roughly half the NFE budget, which would make inference-time scaling more compute-efficient in practice.","The convergence proof extends existing adaptive-SMC guarantees to the time-varying particle count and temperature schedule, so the method inherits principled convergence behavior rather than being a pure heuristic."],"supporting_citations":[{"why":"Supplies the SMC/FK-Steering framework, the Max-potential baseline, and the convergence theory that the paper extends.","marker":"Singhal et al. [2025]"},{"why":"Provides ImageReward, the reward model used both to guide the search and as the primary evaluation metric.","marker":"Xu et al. [2023]"},{"why":"Provides GenEval, the main text-to-image alignment benchmark and metric for the reported gains.","marker":"Ghosh et al. [2023]"},{"why":"Establishes the convergence conditions for adaptive SMC with time-varying particle counts and temperatures, used in the appendix.","marker":"BESKOS et al. [2016]"},{"why":"Supplies the Stable Diffusion 1.5/2.0/2.1 pretrained models on which experiments run.","marker":"Rombach et al. [2022]"},{"why":"Supplies the SDXL pretrained model used as the fourth testbed.","marker":"Podell et al. [2024]"}],"fun_headline_variants":["Funnel schedule and adaptive temperature sharpen diffusion inference scaling","Two simple tweaks make SMC diffusion search explore smarter, exploit better","Exploration-exploitation balance for diffusion inference-time scaling","Funnel schedule and adaptive temperature improve diffusion image alignment","Boosting diffusion sample quality with reward-aware particle scheduling"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire fixed-budget comparison rests on the claim that the funnel schedule $[12,10,6,4,4]$ sums to exactly 240 noise function evaluations over the 30 denoising steps; the paper never states which step intervals use which particle count, so the equal-compute claim is unverified.","fun_headline_variants_meta":{"raw":{"variants":["Funnel schedule and adaptive temperature sharpen diffusion inference scaling","Two simple tweaks make SMC diffusion search explore smarter, exploit better","Exploration-exploitation balance for diffusion inference-time scaling","Funnel schedule and adaptive temperature improve diffusion image alignment","Boosting diffusion sample quality with reward-aware particle scheduling"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000478,"raw_usage":{"total_tokens":2380,"prompt_tokens":967,"completion_tokens":1413,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":583,"completion_tokens_details":{"reasoning_tokens":1333}},"tokens_in":583,"tokens_out":1413,"duration_ms":13087,"temperature":1.0,"reasoning_tokens":1333,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:22:48.060908+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the total NFE: with resampling at timesteps $\\{10,15,20,25,29\\}$ and particle counts $[12,10,6,4,4]$ assigned to the intervals between them, the sum over 30 steps must equal 240. If any natural assignment yields a different total, or if no assignment consistent with the paper's text sums to 240, the performance gain is attributable to a larger compute budget rather than the funnel schedule. Alongside this, re-run F-SMC-A(D) against SMC(D) with 8 particles and 30 steps, both at exactly 240 NFE, to confirm the gain persists under a verifiable budget.","supporting_citations":[],"review_version":2}