{"id":"3104dd06-2912-4194-b789-6aa84e5d4d59","arxiv_id":"2605.18736","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Spectral Progressive Diffusion progressively grows resolution during denoising of pretrained diffusion models via spectral noise expansion and a power-spectrum-derived schedule, enabling training-free speedups and a fine-tuning recipe.","lead":"Diffusion models build images from low to high frequencies during denoising. This paper introduces a framework to progressively increase resolution along that trajectory for faster generation.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Spectral noise expansion must preserve exact per-timestep variance for the pretrained denoiser to remain valid without retraining.","rationale":"The reader correctly flagged the redundancy assumption as weakest, but the load-bearing technical risk is narrower: whether the proposed expansion operator is distribution-preserving enough for the fixed pretrained weights. This is a correctness risk rather than a novelty or empirical issue; confirming the variance match would either validate the training-free claim or force the fine-tuning recipe to be mandatory.","tokens_in":1575,"tokens_out":378,"duration_ms":31346,"concrete_test":"Sample noise at full resolution for a mid-trajectory timestep t using the original variance schedule; apply the paper’s spectral expansion operator from the low-resolution state at t-1; measure the L2 difference in power spectrum and total variance against the direct full-resolution sample. If the discrepancy exceeds the tolerance used in the paper’s own ablation (typically <1% relative error), recompute FID on 5k samples with the mismatched noise and report the quality drop.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The training-free path claims to accelerate by running early denoising steps at low resolution and expanding noise spectrally to higher resolution later. For this to be mathematically sound, the expanded noise at each transition timestep must match the marginal distribution that the original high-resolution diffusion process would have produced. If the expansion operator (described as operating on the power spectrum) does not exactly reproduce the variance schedule and cross-frequency correlations of the pretrained model, the subsequent denoising steps receive inputs outside the training distribution, violating the assumption that the fixed network can be applied unchanged. The abstract states an “optimal resolution schedule from the model’s power spectrum,” but does not indicate whether this schedule is derived under the exact forward-process marginals or only under an empirical average spectrum.","agreement_with_reader":"partial"},"referee_report":{"model":"grok-4.3","summary":"The paper introduces Spectral Progressive Diffusion, a framework for accelerating pretrained diffusion models for image and video generation by progressively growing resolution along the denoising trajectory. It develops a spectral noise expansion mechanism and derives an optimal resolution schedule from the model's power spectrum, supporting both training-free acceleration and a fine-tuning recipe, with claims of significant speedups on SOTA models while preserving visual quality.","tokens_in":1756,"tokens_out":530,"duration_ms":33967,"significance":"If the central claims hold, the work provides a general, practical approach to reducing the computational cost of high-resolution generation without retraining, which is valuable given the expense of diffusion-based image and video models. The emphasis on leveraging implicit frequency-domain structure in pretrained models and the dual training-free/fine-tuning support are strengths that could influence efficiency-focused extensions in generative modeling.","major_comments":[{"comment":"§3 (spectral noise expansion mechanism): The claim that the mechanism enables training-free application of the fixed pretrained denoiser requires that the expanded noise at each resolution transition exactly matches the marginal distribution (variance schedule and cross-frequency correlations) of the original high-resolution forward process at that timestep. The abstract and method description do not provide an explicit verification or derivation showing this preservation, raising a correctness risk for the subsequent denoising steps.","section":"§3"},{"comment":"§4 (optimal resolution schedule derivation): The schedule is stated to be derived from the model's power spectrum, but it is unclear whether the derivation operates under the exact forward-process marginals or relies on empirical averages; if the latter, the schedule may introduce model-specific fitting that undermines the generalizability of the training-free speedup claim.","section":"§4"}],"minor_comments":[{"comment":"The abstract and introduction would benefit from explicit quantitative results (e.g., speedup factors, FID or perceptual metrics on specific models like Stable Diffusion or video variants) to ground the 'significant speedups' and 'preserving visual quality' claims.","section":"Abstract"},{"comment":"Notation for the power spectrum and resolution schedule should be defined with equations early in the method section to improve clarity for readers tracking the frequency-domain arguments.","section":"Method"}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern about variance preservation appears to land as a load-bearing issue given the abstract's description; the manuscript would be strengthened by adding a short proof or empirical check in the supplement. No obvious citation or scope issues."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their constructive and detailed feedback on our manuscript. We have carefully addressed each major comment below with clarifications and planned revisions to improve the rigor and clarity of the presentation.","responses":[{"response":"We thank the referee for identifying this important aspect of the correctness argument. The current manuscript presents the spectral noise expansion mechanism but does not include a self-contained derivation of marginal preservation. In the revised manuscript we will add a formal derivation in §3 showing that the expansion, by construction via the Fourier basis and power-spectrum scaling, exactly reproduces the variance schedule and cross-frequency covariances of the high-resolution forward process at the transition timestep. We will also include a short verification experiment in the appendix that empirically confirms the distributional match before and after expansion.","revision_made":"yes","referee_comment":"[§3] §3 (spectral noise expansion mechanism): The claim that the mechanism enables training-free application of the fixed pretrained denoiser requires that the expanded noise at each resolution transition exactly matches the marginal distribution (variance schedule and cross-frequency correlations) of the original high-resolution forward process at that timestep. The abstract and method description do not provide an explicit verification or derivation showing this preservation, raising a correctness risk for the subsequent denoising steps."},{"response":"We appreciate the referee’s concern about the theoretical grounding and generalizability. The derivation in §4 starts from the exact forward-process marginals and uses the power spectrum to identify the timestep at which high-frequency energy falls below a noise-dominated threshold; the schedule is therefore analytic with respect to those marginals. In practice the power spectrum is estimated once from the pretrained model, but this estimation is not a learned fitting procedure and does not alter the underlying marginals. We will expand §4 to make this distinction explicit, add a short proof sketch linking the schedule directly to the marginal variance expressions, and include a brief discussion of why the same procedure applies to any diffusion model whose frequency-generation ordering is consistent with the observed power-spectrum decay.","revision_made":"partial","referee_comment":"[§4] §4 (optimal resolution schedule derivation): The schedule is stated to be derived from the model's power spectrum, but it is unclear whether the derivation operates under the exact forward-process marginals or relies on empirical averages; if the latter, the schedule may introduce model-specific fitting that undermines the generalizability of the training-free speedup claim."}],"tokens_in":1267,"tokens_out":517,"duration_ms":25715,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main point is that this work makes the implicit frequency progression in diffusion models explicit by starting at low resolution and expanding noise spectrally as denoising advances. They derive a resolution schedule from the model's power spectrum and add a noise expansion step that lets the same pretrained denoiser run at varying resolutions. Both a training-free path and a fine-tuning recipe are presented, with reported speed gains on current image and video generators while keeping visual quality comparable.","headline":"The paper turns the known low-to-high frequency order in diffusion into a progressive-resolution schedule with spectral noise expansion, claiming training-free speedups on image and video models.","tokens_in":2207,"tokens_out":167,"would_cite":false,"duration_ms":21302,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[{"relation":"unclear","rs_module":"IndisputableMonolith/Cost/FunctionalEquation.lean","rs_theorem":"washburn_uniqueness_aczel","paper_passage":"We define the per-frequency signal power... Pω := E[|x0(ω)|²] ... Pω ∝ |ω|^{-β} ... tω := 1 / (1 + sqrt(δ / (Pω(1+Pω−δ)))) ... t*i := minω∈Ωsi tω = tω=si·ωmax(H,W)"},{"relation":"unclear","rs_module":"IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean","rs_theorem":"J_uniquely_calibrated_via_higher_derivative","paper_passage":"spectral noise expansion ... embed ξsi_ti in the lower-frequency part ... fill Ωsi+1∖Ωsi with tiϵ ... timestep alignment ˜ti = (si+1/si)ti / (1+((si+1/si)−1)ti)"}],"headline":"Spectral autoregressive resolution schedule from power-law spectra; no J-cost, φ-ladder or recognition-cost structure","alignment":"orthogonal","rationale":"The paper's core machinery (Proposition 1–2 deriving δ-optimal activation times tω from per-frequency SNRω(t) = (1−t)²Pω/t² under Gaussian modelling, Nyquist-linked resolution transitions, and spectral noise expansion that pads high-frequency slots with tiϵ) is a standard frequency-domain analysis of diffusion trajectories. It exploits the empirical power-law decay Pω ∝ |ω|^{-β} (β≈1.9–2.4) but never invokes the RS reciprocal cost J(x)=½(x+x⁻¹)−1, cosh(ρ ln φ)−1 identities, ratio-symmetric forcing, 8-tick periodicity, or any theorem from the AbsoluteFloorClosure / Cost / DimensionForcing chain. The construction is therefore compatible with but not isomorphic to RS-shaped reasoning.","tokens_in":62047,"confidence":"high","tokens_out":465,"duration_ms":17257,"cache_read_input_tokens":38528,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Diffusion models generate images and videos faster by starting at low resolution and growing it as denoising proceeds from low to high frequencies.","keywords":["diffusion models","image generation","video generation","efficient inference","frequency domain","progressive resolution","spectral noise"],"falsifier":"Running the identical pretrained model at full resolution throughout denoising produces images or videos of equal or higher quality in equal or less wall-clock time than the progressive schedule.","tokens_in":2488,"feed_emoji":"⚡","tokens_out":581,"duration_ms":17476,"temperature":0.7,"pith_summary":"The paper establishes that diffusion models implicitly build visual content from low frequencies early in denoising to high frequencies later. This ordering makes high-resolution computation wasteful in the initial noisy stages. Spectral Progressive Diffusion exploits the pattern by expanding resolution along the trajectory using a spectral noise mechanism and a schedule taken from the model's power spectrum. The approach works on existing pretrained models either without any training or with a lightweight fine-tuning step, delivering measurable speedups on both image and video generators while visual quality remains intact.","feed_headline":"Diffusion models speed up by growing resolution during denoising","feed_subtitle":"Early denoising steps focus on low frequencies, so low-resolution computation suffices until high-frequency details emerge later.","key_machinery":"Spectral noise expansion mechanism that progressively grows resolution along the denoising trajectory according to a schedule derived from the model's power spectrum.","core_discovery":"Diffusion models generate visual content autoregressively in the frequency domain, with low-frequency components appearing earlier in the denoising process and high-frequency details emerging later. High-resolution computation on noise-dominated frequencies is therefore redundant. Spectral Progressive Diffusion progressively grows resolution along the denoising trajectory of pretrained models by means of a spectral noise expansion mechanism and an optimal resolution schedule derived from the model's power spectrum. This framework supports both training-free acceleration and a fine-tuning recipe that further improves efficiency and quality.","pith_inferences":["The method could be combined with existing sampler accelerations such as fewer steps or distillation to compound speedups.","Similar progressive schedules might transfer to other generative paradigms that exhibit frequency ordering during synthesis.","Real-time or edge-device deployment becomes more feasible once early low-resolution stages replace full-resolution passes."],"forward_implications":["Pretrained image and video diffusion models can be accelerated without retraining.","A lightweight fine-tuning stage yields further gains in speed and output quality.","The same frequency-progression logic applies across both static images and temporal video sequences.","Compute savings scale with the length of the denoising trajectory and the chosen resolution schedule."],"fun_headline_variants":["Resolution grows progressively in diffusion denoising","Spectral method grows resolution along denoising trajectory","Progressive resolution growth along denoising trajectory","Spectral noise expansion enables resolution scaling in diffusion"],"cache_read_input_tokens":64,"weakest_assumption_plain":"High-resolution computation on noise-dominated frequencies is largely redundant.","fun_headline_variants_meta":{"raw":{"variants":["Resolution grows progressively in diffusion denoising","Spectral method grows resolution along denoising trajectory","Progressive resolution growth along denoising trajectory","Spectral noise expansion enables resolution scaling in diffusion"]},"model":"grok-4.3","cost_usd":0.014004,"raw_usage":{"total_tokens":5919,"prompt_tokens":581,"num_sources_used":0,"completion_tokens":50,"cost_in_usd_ticks":140040500,"prompt_tokens_details":{"text_tokens":581,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":5288,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":581,"tokens_out":50,"duration_ms":58494,"temperature":1.0,"reasoning_tokens":5288,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-21T07:48:36.978396+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Running the identical pretrained model at full resolution throughout denoising produces images or videos of equal or higher quality in equal or less wall-clock time than the progressive schedule.","supporting_citations":[],"review_version":2}