{"id":"f8dbe51d-8634-48d8-94cc-7213e928f002","arxiv_id":"2412.09328","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"ARMD replaces noise in diffusion models with a deterministic sliding of the series window, turning denoising into iterative forecasting, and reports SOTA results on 12 of 14 diffusion-baseline settings.","lead":"A new time series forecasting model called ARMD reinterprets diffusion as a sliding chain from future to historical data, then reverses that chain to predict the future. The authors report faster and more stable forecasts than existing diffusion-based models on seven benchmarks, though the gains over strong non-diffusion baselines are mixed.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (8) is not the inverse of the sliding forward process even with an oracle trend predictor: with z_hat = z_t it yields sqrt(alpha_{t-1}) X^0 + sqrt(1-alpha_{t-1}) z_t, while the true next state uses z_{t-1}; the diffusion chain is therefore not a valid DDIM reverse process.","rationale":"The paper's headline claim is threefold: empirical SOTA over diffusion baselines, first continuous sequential diffusion model, and reverse process aligned with TSF. The weakest load-bearing support is the reverse update, because the empirical advantage could be coincidental to the architecture, but the theoretical contribution depends on Equation (8). The concern is not about consensus; it is an algebraic inconsistency. One might object that a generative model need not match forward intermediates, since DDIM itself uses a non-Markovian process that can skip steps, but DDIM's update is designed to keep a fixed noise epsilon through the chain; here z_t is redefined at every t by Equation (3) and differs at adjacent steps. With oracle prediction the update already fails to reconstruct the sliding state, so the reverse process is not a denoising of the forward process. This directly undermines the 'continuous sequential diffusion' claim and the 'state-of-the-art diffusion' framing, though the numerical results in Tables 1-4 could still be reproducible. A conditional acceptance with mandatory demonstration, or derivation, of reversibility is appropriate: the formal status of Equation (8) must be fixed and claims adjusted. The reader's weakest assumption already targeted this same step; the present check makes it decisive, so the reader's conditional verdict remains the right recommendation.","tokens_in":15422,"tokens_out":8177,"duration_ms":85429,"concrete_test":"On any held-out batch (e.g., ETTm1 test), compute true forward states X^t for t = T-1, ..., 1 from the data, since they are just shifted windows. Feed the true X^t into the trained R, but replace the network's predicted z_hat by the oracle z_t from Equation (3); apply Equation (9) with sigma_t = 0, and compare the result to the true X^{t-1}. If the relative L2 error is not zero, or equivalently if ||z_t - z_{t-1}|| > 0, Equation (9) is not the inverse of Equation (1). This one check separates 'DDIM-compatible diffusion' from 'heuristic iterative refinement' without retraining.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Under the forward definition, X^t_i is the series value at global time i - t, so exact one-step inversion must return X^{t-1}_i = value at i - t + 1. Equation (2) writes X^t = sqrt(alpha_t) X^0 + sqrt(1 - alpha_t) z_t and defines z_t by Equation (3). Substitute the oracle predictor z_hat(t, theta) = z_t into Equation (9) with sigma_t = 0 (as the deterministic sampler sets): X^{t-1}_rec = sqrt(alpha_{t-1}) X^0 + sqrt(1 - alpha_{t-1}) z_t. But the true forward state is X^{t-1} = sqrt(alpha_{t-1}) X^0 + sqrt(1 - alpha_{t-1}) z_{t-1}. Since z_t is not equal to z_{t-1} for a sliding window, Equation (9) cannot invert Equation (1). This is internal, not a question of training convergence; it holds for a perfect network. Thus the reverse/sampling loop in Algorithm 2 is not a principled DDIM/DDPM denoising chain. The claimed 'continuous sequential diffusion' architecture may still function as an iterative forecaster, but the diffusion-mechanism justification and the 'first continuous sequential diffusion' novelty claim require the reverse transition to be derived, not borrowed from DDIM. Fixed-epsilon DDIM requires the same epsilon at every step; ARMD's z_t changes at every step, so the analogy breaks.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Auto-Regressive Moving Diffusion (ARMD), a deterministic diffusion-style model for multivariate time series forecasting. The forward process slides a future window toward a historical window over T steps, and a residual variable z_t is defined so that the state X^t satisfies a DDPM-like scaling equation. A linear network is trained to predict z_t from the current state, and sampling is performed by iterating a DDIM-style update, starting from the historical series and ending at the predicted future series. The paper claims state-of-the-art results on seven benchmarks, reports a large speed-up relative to noise-based diffusion forecasters, and identifies ARMD as the first continuous sequential diffusion-based TSF model.","tokens_in":15795,"tokens_out":8756,"duration_ms":91514,"significance":"If the method and its theoretical framing were sound, ARMD would be a valuable contribution: it is simple, fast, deterministic, and the released code would facilitate reproduction. The reported 10x+ training and inference speed-ups over diffusion baselines are practically relevant, and the empirical wins in Table 1 are substantial. However, the paper's central claim to be a diffusion model is currently not supported by the derivations: the forward process in Eqs. (2)-(3) is a deterministic re-labeling, and the reverse update in Eq. (8) is not a valid inverse of the forward process even with a perfect network. The experimental evidence also lacks error bars and uses an asymmetric tuning protocol. These issues are load-bearing for the paper's novelty and for its \"state-of-the-art diffusion model\" claim.","major_comments":[{"comment":"Equation (3) defines z_t as the residual that makes Eq. (2) an identity: z_t is a deterministic function of X^t and X^0, so the forward process contains no stochastic diffusion and no learned representation of noise. The training target in Eq. (7) is therefore a deterministic regression target rather than a denoising objective. This does not by itself invalidate the method, but it means the claimed analogy to DDPM and the \"continuous sequential diffusion\" novelty must be justified by a derived forward/reverse pair, not by an algebraic re-parametrization.","section":"Forward Diffusion (Evolution) of ARMD, Eqs. (2)-(3)"},{"comment":"Equation (9) is not the inverse of Eq. (1) even with an oracle predictor. Substituting \\hat z(t,\\theta)=z_t and \\sigma_t=0 into Eq. (9) yields X^{t-1}_{rec} = \\sqrt{\\bar\\alpha_{t-1}} X^0 + \\sqrt{1-\\bar\\alpha_{t-1}} z_t, whereas the true forward state is X^{t-1} = \\sqrt{\\bar\\alpha_{t-1}} X^0 + \\sqrt{1-\\bar\\alpha_{t-1}} z_{t-1}. For sliding windows, z_t \\neq z_{t-1} in general, so the update cannot invert the forward process even with a perfect network. Thus Algorithm 2 is not a principled DDIM/DDPM denoising chain. The authors need to derive a valid reverse transition from the forward process, or prove that the iterative refinement converges to X^0; otherwise the diffusion-based framing and the \"first continuous sequential diffusion\" claim are unsupported.","section":"Sampling/Forecasting of ARMD, Eqs. (8)-(9)"},{"comment":"The supplement states that ARMD's sampling steps are selected by grid search on the validation set from {1,2,3,4,6,8,12}, while all other diffusion baselines use the default sampling steps of 100. This is an asymmetric comparison: ARMD is tuned on validation, whereas the baselines are not given the same tuning opportunity. Since Tables 1 and 2 report no error bars or confidence intervals despite averaging over 10 sampling runs, the claim of \"significantly outperforming\" existing models is not statistically supported. Please report standard deviations or intervals and use a comparable tuning budget for all methods.","section":"Supplement, Experiment Details"},{"comment":"The comparison with non-diffusion TSF models in Table 2 is mostly sourced from the iTransformer paper rather than from a common experimental protocol. Different data splits, normalization, and hyperparameter choices can change MSE/MAE materially. The authors should either re-run all baselines under the same protocol or clearly annotate the source of each number and justify comparability.","section":"Table 2 and experimental protocol"},{"comment":"The claim that the linear backbone outperforms the Transformer backbone is weakened by Table 4: the Transformer backbone achieves better MSE on ETTh2, ETTm2, and Stock, and is close on Solar and Exchange. The aggregate \"11 out of 14\" count does not establish robustness without significance testing or an analysis of when the linear backbone is preferable. Please temper the claim or provide statistical support.","section":"Ablation Studies, Table 4"}],"minor_comments":[{"comment":"The vector addition in Eq. (2) is ambiguous because X^t_{1-t:T-t} and X^0_{1:T} have different index ranges. Please specify the alignment convention used in the implementation.","section":"Notation, Eqs. (2)-(3)"},{"comment":"The main text refers to \"Equation (14)\" for the DDPM forward formula, but Eq. (14) appears in the supplemental material; please renumber or cite the supplement explicitly.","section":"Equation numbering"},{"comment":"Table 3 reports training and inference time in seconds but does not state whether training time is per epoch, per 2,000 iterations, or a full run; please clarify the measurement and include units for both phases.","section":"Table 3"},{"comment":"The hyper-parameters b, c, and d in Eq. (5) are selected by grid search per dataset, but the selected values are not reported. Please provide the chosen values and a sensitivity analysis.","section":"Supplement, Hyper-parameters"}],"recommendation":"major_revision","confidential_remarks":"The paper has a useful empirical component and a clean code release, but the central theoretical issue in Eqs. (8)-(9) should be resolved before the manuscript can be accepted as a diffusion-model paper. If the authors cannot provide a valid reverse-process derivation, they should reposition the work as a deterministic iterative forecaster and remove the diffusion-based novelty claims. The asymmetric tuning of sampling steps and the absence of error bars should also be addressed in any revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version: ARMD is not really a diffusion model in the DDPM/DDIM sense, but it is a real, simple, fast forecasting method. What is new is the sliding-window chain: instead of adding noise, the future window is shifted backwards step by step until it becomes the history, and a linear network is trained to predict the residual z_t at each step. That deterministic construction is genuinely different from TimeDiff, MG-TSD, and the other cited diffusion TSF models, and the reported speedup (roughly 10x) is a real practical point in its favor. The empirical tables are broad, the ablation clearly favors sliding over interpolation and the linear backbone over a Transformer, and the method is simple enough to reproduce.\n\nThe soft spots are real and one is load-bearing. Your stress-test is correct: with an oracle trend predictor, Eq. (9) does not recover the previous sliding state. It gives sqrt(alpha_{t-1}) X^0 + sqrt(1-alpha_{t-1}) z_t, whereas the true X^{t-1} uses z_{t-1}. In DDIM the same epsilon is reused across steps; here z_t changes at every step, so the borrowed update is not a principled inverse of the forward process. This is internal, holding even for a perfect network. So the 'continuous sequential diffusion' framing and the 'first' claim need serious reworking. The authors should either derive a correct inverse for the sliding chain or reframe the model as iterative refinement.\n\nSecond, the SOTA claim is too strong. Table 2 shows iTransformer beats ARMD on ETTh1, ETTh2, ETTm1, ETTm2, and Exchange. Winning among diffusion baselines is fine, but 'state-of-the-art' overall does not hold. Also, there are no error bars even though the diffusion baselines are stochastic; the comparison should report uncertainty for both sides.\n\nThe ARMA connection is an analogy, not a derivation, and Equation (5) has three hyperparameters selected per dataset with no sensitivity analysis. That is a minor weakness, not a fatal one.\n\nWho should read this: people working on fast deterministic alternatives to diffusion TSF will get a useful trick. As a diffusion paper, it needs major revision. Recommendation: send it to peer review, because the construction is novel and the empirical study is broad, but the reviewer should push hard on Eq. (8)/(9). If the authors cannot justify that step, the diffusion framing should be dropped and the paper resubmitted as an iterative forecaster.","headline":"ARMD is a clever deterministic sliding-window iterative forecaster wearing a diffusion costume, and the costume does not fit: the borrowed DDIM reverse update is not a valid inverse of the forward sliding chain.","tokens_in":16332,"tokens_out":4160,"would_cite":false,"duration_ms":40248,"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":"ARMD replaces Gaussian noise with a deterministic slide from future to past, and reports state-of-the-art forecasting across 12 of 14 benchmark settings.","keywords":["diffusion models","time series forecasting","auto-regressive moving average","sliding diffusion","multivariate forecasting","deterministic sampling"],"falsifier":"Train the same linear devolution network to predict the future series directly in a single step, bypassing the iterative sampling; if single-step prediction matches or beats the multi-step ARMD results on identical benchmarks, then the diffusion or iterative-refinement machinery is not what drives the reported gains. Alternatively, apply the forward slide to a synthetic series and check whether the DDIM update exactly recovers the previous sliding state at an intermediate step; any mismatch means the reverse process is not a faithful inverse.","tokens_in":1819,"feed_emoji":"📈","tokens_out":1881,"duration_ms":73018,"temperature":0.7,"pith_summary":"This paper argues that standard diffusion-based forecasting is misaligned with the continuous, sequential nature of time series because it corrupts the data into Gaussian noise and conditions on history. It proposes ARMD, a diffusion model whose forward process deterministically slides the future series toward the historical series, so that intermediate states are meaningful intermediate windows. The reverse process, a linear devolution network, reverses this slide and makes forecasting an unconditional, deterministic sampling procedure. Across seven multivariate benchmarks, ARMD wins 12 of 14 settings against diffusion-based baselines and also outperforms strong non-diffusion forecasters, while cutting training and inference time by more than tenfold.","feed_headline":"Slide-based diffusion model wins 12 of 14 forecasting benchmarks","feed_subtitle":"A deterministic diffusion that slides the future into the past beats noise-based rivals and runs ten times faster.","key_machinery":"The central mechanism is a sliding-based forward process that replaces noise addition with a deterministic shift: $X^t_{1-t:T-t} = \\mathrm{Slide}(X^0_{1:T}, t)$, and the evolution trend $z_t$ is defined post hoc by Equation (3) as the discrepancy between the slid window and the future target under the DDPM scaling. The reverse sampling step adapts the DDIM update (Equation 8) to this trend and removes the stochastic noise term, making sampling deterministic. The other load-bearing component is the linear devolution network $R(.)$, which predicts the distance $D$ from the current window to the target and combines it with the input through a time-dependent weight $W(t)$.","core_discovery":"ARMD is introduced as the first continuous sequential diffusion-based time series forecasting model. The future series $X^0_{1:T}$ is the initial diffusion state, the historical series $X^T_{-T+1:0}$ is the final state, and each intermediate state $X^t_{1-t:T-t}$ is obtained by sliding the future window $t$ steps toward the past. The reverse process adapts the DDIM sampling update, replacing predicted noise with a predicted evolution trend $\\hat{z}(t,\\theta)$ that is defined through the DDPM interpolation formula. The devolution network is a linear module that estimates the distance from the current window to the target and combines it with the input via a time-dependent weight, initialized from the DDPM coefficients $\\bar{\\alpha}_t$ and trained end-to-end. The paper reports that this design aligns diffusion with the natural evolution of time series, yielding a faster, more stable, and more accurate forecaster than existing noise-based diffusion models.","pith_inferences":["A natural extension the paper does not take: the same sliding-diffusion idea could transfer to other ordered-sequence domains such as language or video, where past and future have a clear temporal ordering, though the paper does not demonstrate this.","A reader should be cautious that the state-of-the-art claim is inseparable from the strength of the linear backbone; the paper's ablations do not isolate whether the iterative diffusion step itself adds accuracy over a single direct linear prediction.","Because the forward process is deterministic and sampling noise is removed, ARMD does not naturally provide calibrated probabilistic forecasts; a user requiring uncertainty quantification would need to extend the method, which the paper does not address.","The post hoc definition of the trend term $z_t$ means the diffusion is effectively a deterministic interpolation schedule; the paper's framing as a true denoising process is an interpretation rather than a derived generative model."],"forward_implications":["If ARMD's claims hold, diffusion-based forecasting no longer requires stochastic sampling: forecasts are deterministic and reproducible, and sampling steps can be skipped to reduce inference cost.","The reported tenfold reduction in training and inference time would make diffusion-based forecasting practical for long series and high-dimensional multivariate data.","The ablation results indicate that the sliding-based intermediate states, the distance-based linear devolution, and the absence of sampling noise each contribute to the reported performance gains.","The alignment of diffusion states with actual time-series evolution suggests a design principle: the diffusion path should match the semantics of the data domain rather than being a generic noise-corruption schedule.","The unconditional formulation removes the need for a separate conditioning network, simplifying the forecasting pipeline while improving stability."],"supporting_citations":[{"why":"Supplies the DDPM forward and reverse equations that ARMD adapts to its sliding-based diffusion.","marker":"(Ho, Jain, and Abbeel 2020)"},{"why":"Provides the DDIM sampling update that ARMD uses for its deterministic reverse process.","marker":"(Song, Meng, and Ermon 2020)"},{"why":"CSDI is a primary diffusion-based baseline that ARMD compares against and outperforms.","marker":"(Tashiro et al. 2021)"},{"why":"TimeDiff supplies notation for diffusion states and serves as a non-autoregressive diffusion baseline.","marker":"(Shen and Kwok 2023)"},{"why":"TimeGrad is an autoregressive diffusion baseline that ARMD claims to surpass in accuracy and speed.","marker":"(Rasul et al. 2021)"},{"why":"Diffusion-TS is the main comparison model in both quantitative tables and qualitative stability analysis.","marker":"(Yuan and Qiao 2024)"},{"why":"MG-TSD provides a multi-granularity diffusion baseline that ARMD outperforms on most datasets.","marker":"(Fan et al. 2024)"},{"why":"TSDiff is a self-guiding diffusion baseline used in the benchmark comparison.","marker":"(Kollovieh et al. 2024)"},{"why":"D3V AE is a diffusion-denoising-disentanglement baseline that ARMD beats on several settings.","marker":"(Li et al. 2022)"}],"fun_headline_variants":["Sliding diffusion turns forecasting into continuous evolution","Future-state diffusion slides history to forecast better","Diffusion from future to past beats noise-based forecasting","ARMD aligns diffusion with time series evolution","Chain-based diffusion outperforms noise-based time series models"],"cache_read_input_tokens":18304,"weakest_assumption_plain":"The sampling update borrowed from DDIM is assumed to correctly reverse the deterministic sliding forward process, even though the forward process is not noise-based and the trend term $z_t$ is defined after the fact rather than derived from a generative model.","fun_headline_variants_meta":{"raw":{"variants":["Sliding diffusion turns forecasting into continuous evolution","Future-state diffusion slides history to forecast better","Diffusion from future to past beats noise-based forecasting","ARMD aligns diffusion with time series evolution","Chain-based diffusion outperforms noise-based time series models"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00098,"raw_usage":{"total_tokens":4190,"prompt_tokens":1007,"completion_tokens":3183,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":623,"completion_tokens_details":{"reasoning_tokens":3113}},"tokens_in":623,"tokens_out":3183,"duration_ms":23227,"temperature":1.0,"reasoning_tokens":3113,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T17:05:56.653748+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train the same linear devolution network to predict the future series directly in a single step, bypassing the iterative sampling; if single-step prediction matches or beats the multi-step ARMD results on identical benchmarks, then the diffusion or iterative-refinement machinery is not what drives the reported gains. Alternatively, apply the forward slide to a synthetic series and check whether the DDIM update exactly recovers the previous sliding state at an intermediate step; any mismatch means the reverse process is not a faithful inverse.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"CSDI is a primary diffusion-based baseline that ARMD compares against and outperforms."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"TimeDiff supplies notation for diffusion states and serves as a non-autoregressive diffusion baseline."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"TimeGrad is an autoregressive diffusion baseline that ARMD claims to surpass in accuracy and speed."}],"review_version":1}