{"id":"3462f55d-f88f-4535-ae50-f792de0240be","arxiv_id":"2507.06656","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"SPGD combines a progressive likelihood warm-up with adaptive directional momentum to reduce gradient conflicts and fluctuations in diffusion-based image restoration, improving metrics over existing baselines.","lead":"This paper introduces SPGD, a training-free technique that stabilizes diffusion models for image restoration by splitting likelihood guidance into small warm-up steps with adaptive momentum smoothing. The authors report improved PSNR, SSIM, and LPIPS across inpainting, deblurring, and super-resolution on FFHQ and ImageNet.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Primary DPS comparison is confounded: Table 1 DPS uses DDPM/T=1000 while SPGD uses EDM/T=100, and Table 2's own baseline shows a ~4 dB schedule-driven gap, so the SOTA-over-DPS claim is not isolated.","rationale":"I read the paper as making two related claims: (1) the reverse process suffers from gradient conflict and fluctuation, and (2) SPGD's warm-up plus ADM mitigates these to yield state-of-the-art restoration. The empirical support for (2) is the load-bearing part, because the paper's own theoretical result (Proposition 4.1) is a generic descent lemma for gradient descent on the likelihood objective and does not establish that reducing likelihood early improves final perceptual quality. The reader's weakest-assumption analysis correctly identified the DPS comparison as confounded: the baseline in Table 2 is DPS-like but uses EDM/T=100, while Table 1's DPS row uses DDPM/T=1000, and Appendix D confirms these settings differ. This matters because the schedule and step-count change alone can produce several dB of difference in diffusion restoration, and the paper explicitly acknowledges the discrepancy in a footnote. The ablation in Table 2 does provide controlled evidence that warm-up improves over the same-schedule baseline, so I would not reject the method; however, the headline state-of-the-art claim versus DPS is not currently isolated. A single reproduced DPS run under the same schedule and budget would settle whether the advantage is real. Therefore the appropriate verdict remains CONDITIONAL, matching the reader's assessment.","tokens_in":23697,"tokens_out":3449,"duration_ms":40552,"concrete_test":"Run DPS with the exact SPGD settings (EDM schedule, T=100, N=1, ζ tuned per task using Table 5) on the same full FFHQ and ImageNet test sets used for Table 1, and compare PSNR/SSIM/LPIPS against SPGD at the same total NFE budget. If the resulting DPS numbers approach the Table 2 baseline and come within roughly 0.5 dB of SPGD, the Table 1 DPS comparison is invalidated; if SPGD still maintains its margin, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that SPGD achieves state-of-the-art performance over DPS rests on Table 1, but the DPS numbers there are produced with the original DDPM schedule at 1,000 steps (Appendix D), whereas SPGD uses the EDM schedule with T=100 and N=5 warm-up steps. Table 2's \"baseline\" (warm-up and ADM both off) is effectively DPS under SPGD's improved experimental settings, and it already reaches 30.35 PSNR on FFHQ inpainting versus 26.11 for DPS in Table 1; Table 3 shows the same T=100/N=1 baseline at 30.357. This 4.2 dB gap is comparable to the entire claimed improvement of SPGD over DPS (30.87 versus 26.11). Footnote 2 attributes the discrepancy to \"improved experimental settings\" but never reports a DPS variant using the same EDM schedule, step count, and per-task ζ tuning on the full test set. Figure 6 and Table 3 likewise compare SPGD (EDM, T=100) with DPS (DDPM, T=500 or T=1000) under different schedules, so the improvement over DPS cannot be attributed to the proposed gradient management components. The ablation does show that warm-up helps over the shared-schedule baseline, which is genuine evidence for the method, but the headline state-of-the-art claim relative to DPS is not isolated from the schedule change.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies instability in DPS-style diffusion models for image restoration, attributing it to two gradient-level phenomena: directional conflict between the denoising gradient g_d and the likelihood gradient g_l in early reverse stages, and temporal fluctuation of g_l in intermediate stages. To address these, the authors propose SPGD, which combines (1) a progressive warm-up phase that performs N small likelihood-only gradient steps before each DDIM denoising step, and (2) Adaptive Directional Momentum (ADM) smoothing, which weights the momentum coefficient by the cosine similarity between successive likelihood gradients. The theoretical support is a descent lemma (Proposition 4.1) proving that the warm-up phase decreases the per-timestep likelihood objective under an L-smoothness condition when momentum is disabled. Experiments on FFHQ and ImageNet cover random inpainting, Gaussian and motion deblurring, and 4x super-resolution, with ablations over the design components, the inner step count N, and the momentum base coefficient β. The paper claims state-of-the-art quantitative results and improved generation stability, and the authors release code. The central empirical evidence for the method itself is the ablation table, but the headline comparison against DPS is confounded by a change of sampling schedule and step count.","tokens_in":23981,"tokens_out":20083,"duration_ms":176142,"significance":"The proposed warm-up plus adaptive-momentum recipe is simple, easy to implement on top of existing DPS-style solvers, and the ablation evidence (Table 2) shows a real gain over a shared-schedule baseline: roughly 1.3 dB PSNR on FFHQ inpainting and 1.7 dB on SRx4 at T=100, with consistent SSIM and LPIPS improvements. The paper ships code, reports per-task hyperparameters (Table 5), and gives a complete, checkable proof of its descent lemma, which is a genuine strength. If the controlled comparisons confirm the magnitude of the gain, the warm-up idea is a useful and immediately applicable contribution. However, the current experimental presentation substantially overstates what is established: the state-of-the-art claim over DPS is entangled with a schedule and step-count change whose effect (~4.2 dB on FFHQ inpainting) is several times larger than the method's own contribution, and one of the paper's central summary sentences is contradicted by its own Table 1. The proposition is correct but does not connect likelihood descent to final restoration quality, a limitation the paper's own N=20 ablation illustrates.","major_comments":[{"comment":"The paper's headline claim of state-of-the-art performance over DPS rests on a comparison that is not isolated from a sampling-schedule change. Table 1 reports SPGD under the EDM schedule with T=100 and N=5 (Appendix D.2) against DPS numbers reproduced from the original DDPM 1000-step implementation (Appendix D.1), whereas the Table 2 ablation baseline, a single DPS-style likelihood correction per denoising step under SPGD's own EDM/T=100 settings, already attains 30.35 dB PSNR on FFHQ inpainting compared with 26.11 dB for DPS in Table 1; Table 3's T=100, N=1 row (30.357 dB) confirms the baseline value. Footnote 2 attributes this ~4.2 dB gap to 'improved experimental settings,' but the manuscript never reports a DPS or N=1 variant under the same EDM schedule, the same T=100 step count, the same per-task ζ values, and the full 1,000-image test set. Since the schedule and step-count change accounts for by far the larger part of the 4.76 dB gap between SPGD and DPS in Table 1, the claimed advantage of the proposed gradient management components over DPS is not established as reported and needs a controlled comparison or a reframed claim.","section":"§5.1, Table 1, Table 2 footnote, Appendix D"},{"comment":"The sentence 'On the FFHQ dataset, our method achieves the best results for all metrics across all four degradation types' is contradicted by the numbers in Table 1. For SRx4, DDRM's PSNR (29.49) and SSIM (0.853) both exceed SPGD's (29.35 and 0.831); for Gaussian deblurring, DPPS (0.793), DPS (0.782), and DDRM (0.779) all report higher SSIM than SPGD (0.775). The ImageNet statements in the same section are more carefully qualified, but the FFHQ sentence and the abstract's unconditional 'state-of-the-art performance' wording should be corrected to match the table, for example by stating that SPGD achieves the best results on most metrics with the DDRM and DPPS exceptions noted.","section":"§5.2, Table 1"},{"comment":"Proposition 4.1 is a correct but generic descent lemma for L-smooth objectives, and as theoretical support for SPGD it is limited in three specific ways. First, it covers only the β=0 (no-momentum) configuration, whereas the method's default β=0.95 with the ADM recursion of Eqs. (12)-(13) is precisely the component claimed to damp likelihood-gradient fluctuation, and Appendix C.3 concedes that a convergence analysis of the full method is out of scope. Second, the step-size hypothesis η < 1/L is never verified for the actual experimental choices (ζ/N with ζ between 1 and 8), since no Lipschitz constant L is estimated or bounded. Third, and most importantly, the proposition establishes descent only in the per-timestep likelihood objective L_t, which is by construction the quantity the warm-up is designed to decrease, and the paper's own N=20 ablation (Table 3: PSNR drops to 29.90 from 31.63 at N=5) shows that continuing to decrease that objective can degrade final restoration quality. The proposition therefore does not connect likelihood descent to final PSNR/SSIM/LPIPS, and the sentence claiming that it shows SPGD yields a better estimate x-hat_0 should be scoped explicitly to the likelihood objective.","section":"§4.3, Proposition 4.1, Appendix B, Table 3 (N=20 row)"},{"comment":"The DPS reference rows in Table 3 (T=500 and T=1000 with N=1) are not specified as to sampling schedule, ζ tuning, or update order relative to the SPGD configuration, so the reader cannot tell whether the comparison is controlled; the T=100/N=1 value of 30.357 matching the EDM-based Table 2 baseline suggests these rows do not use the original DDPM schedule of the Table 1 DPS implementation. Under that reading, SPGD at 500 NFEs (31.631 dB) surpasses the T=1000 reference (31.608 dB) by only 0.023 dB PSNR, which does not support the text's 'significantly outperforms ... and even surpasses' wording. Figure 6 likewise compares SPGD (T=100, N=5) with a T=500 curve on a timestep axis, conflating the gradient-management effect with the different outer-step discretization; a matched comparison at equal T, equal NFEs, and clearly stated schedules is required before the efficiency claim can be assessed.","section":"§5.4.2, Table 3, Figure 6"}],"minor_comments":[{"comment":"The sentence 'All experiments are conducted using the same pre-trained models and a fixed random seed to ensure fair comparisons' is at odds with Appendix D.1, which specifies that DPS outcomes come from the original 1,000-step DDPM implementation; the sentence should state explicitly what is matched (checkpoints, seeds) and what is not (schedule, step count, guidance hyperparameters).","section":"§5.1, Appendix D.1"},{"comment":"The claims of 'significant' gradient conflict and fluctuation are supported only by single-sample angle traces without averaging or dispersion; reporting per-dataset mean angle trajectories with error bars, and quantifying the fluctuation claim (for example, the mean absolute change of consecutive g_l angles) with a before/after ADM comparison, would make the diagnostic section falsifiable.","section":"§3.2, Figure 2"},{"comment":"The 'ADM-only' ablation variant in Table 2 is not specified anywhere in Algorithm 1 or the appendix, and the explanation in §5.4.1 describes momentum as accumulating across outer timesteps (t-1, t, ...), while Algorithm 1 re-initializes the momentum buffer at every outer step (lines 5-6); the variant's update rule must be pinned down for the synergy claim to be reproducible.","section":"§5.4.1, Algorithm 1"},{"comment":"The text refers to the comparison curve as 'DPS (T=500)' while the figure caption calls it 'the baseline without gradient management (T=500)'; these are different objects, and the horizontal axis should be expressed in NFEs rather than timesteps to match the 'same NFEs' argument, since SPGD uses T=100 and the reference uses T=500.","section":"§5.4.2, Figure 6"},{"comment":"The phrase 'The another category of methods' is ungrammatical, and the likelihood gradient in Eq. (9) is displayed with the ζ factor while the g_l notation in Algorithm 1 denotes the unweighted gradient; the paper should state explicitly that ζ is applied in the update rule to avoid confusion.","section":"§2.2, Equation (9)"},{"comment":"The novelty discussion mentions the authors' own prior work on history-gradient updates (ref. [17]) but does not specify the algorithmic difference between that momentum/history mechanism and the proposed ADM beyond the adaptive weight in Eq. (13); a concrete comparison would clarify the contribution over [17].","section":"Appendix C.1"}],"recommendation":"major_revision","confidential_remarks":"To the editor: the DPS baseline is evaluated under the original DDPM 1000-step recipe while SPGD is evaluated under the EDM/T=100 recipe with per-task ζ tuning; combined with the ~4.2 dB gap between the Table 2 baseline and Table 1's DPS, the headline comparison currently looks stacked in the method's favor. The revision path is clear: report the N=1/no-warm-up configuration under the same EDM schedule, step count, ζ values, and full test set as SPGD, and adjust the abstract and §5.2 wording to match the tables. The relationship to the authors' own adjacent prior work (refs. [17] and [57]) should be delineated concretely, as Appendix C.1 currently gestures at the difference without specifying it. The core warm-up idea is defensible on the basis of Table 2, so I see this as fixable within the manuscript's scope rather than a rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is a useful, workmanlike addition to training-free diffusion restoration. The core recipe—progressive likelihood warm-up plus adaptive directional momentum—is new as a combination, and the ablation on a shared schedule shows warm-up genuinely helps: on FFHQ inpainting, warm-up lifts PSNR from 30.35 to 31.57 on the same EDM/T=100 setup. That is real evidence. The gradient-angle analysis in Figure 2 is a nice empirical observation, even though it doesn't by itself prove the method works. The theory is a correct but generic descent lemma for L-smooth objectives; as the paper admits in Appendix C, it does not connect descent of the likelihood objective to final image quality. That is a minor limitation given the empirical focus.\n\nThe serious soft spot is the headline comparison to DPS. The DPS numbers in Table 1 are produced with the original DDPM schedule at 1,000 steps (Appendix D), while SPGD uses the EDM schedule with T=100 and N=5. The paper's own baseline in Table 2—warm-up and ADM both off—already reaches 30.35 PSNR on FFHQ inpainting versus 26.11 for DPS in Table 1. That 4.2 dB gap is roughly the entire claimed improvement of SPGD over DPS (30.87 vs 26.11). The footnote blames 'improved experimental settings' but never reports a DPS variant with the same EDM schedule, step count, and task-specific zeta. So the state-of-the-art claim over DPS is not isolated from the schedule change. The same confound applies to Figure 6 and Table 3, where DPS runs at T=500 or T=1000. The trustworthy comparison is the shared-schedule ablation, and it does support warm-up.\n\nA few small things: no error bars, and the ablation of ADM alone shows it hurts, which is consistent with the story but undersells the necessity of the combination. Also, the paper is honest about the theory's limits, which I appreciate.\n\nWho is this for? Practitioners who want a training-free plug-in for diffusion restoration. It deserves a serious referee: the method is reasonable, the warm-up effect is real, and the confound is fixable with a controlled DPS baseline on the same schedule plus a few runs for error bars. I'd send it to review rather than desk reject. If the controlled comparison holds up, the paper becomes a solid subfield contribution.","headline":"Useful training-free stabilizer with a real warm-up win, but the SOTA-over-DPS claim is confounded by an unisolated schedule change.","tokens_in":24546,"tokens_out":2275,"would_cite":false,"duration_ms":22091,"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":"The paper claims that diffusion-based image restoration is limited by conflicts and fluctuations between the denoising and likelihood gradients, and that SPGD's warm-up and adaptive momentum fix this, yielding state-of-the-art results on…","keywords":["diffusion models","image restoration","inverse problems","gradient dynamics","likelihood guidance","momentum smoothing","progressive warm-up","posterior sampling"],"falsifier":"Run the original DPS solver under exactly the same conditions as SPGD—EDM schedule, $T=100$ outer steps, one likelihood update per step—on the same 1,000 FFHQ test images, and compare PSNR, SSIM, and LPIPS with full SPGD. If the metrics match or the gap largely disappears, the warm-up and ADM components are not the cause of the improvement; the schedule change is.","tokens_in":23472,"feed_emoji":"🖼️","tokens_out":11531,"duration_ms":108177,"temperature":0.7,"pith_summary":"The paper tries to establish that diffusion-based image restoration fails in part because of the way its two gradients interact, not just because of how the likelihood is approximated. Analyzing the reverse update as $x_{t-1} = x_t/\\sqrt{\\alpha_t} - g_d(x_t) - \\zeta g_l(x_t)$, the authors report that the denoising gradient $g_d$ and the likelihood gradient $g_l$ point in conflicting directions early in generation, and that $g_l$ fluctuates sharply between consecutive steps. They propose SPGD, which runs several small likelihood-only updates before each denoising step and smooths the likelihood gradient with an adaptive directional momentum term. If the argument is right, this simple gradient management improves restoration quality across inpainting, deblurring, and super-resolution without retraining the diffusion model, and does so at 500 function evaluations rather than 1,000.","feed_headline":"Two gradient fixes beat prior diffusion solvers at image restoration","feed_subtitle":"Warm-up likelihood steps and adaptive momentum stabilize the reverse process on FFHQ and ImageNet.","key_machinery":"The reverse-update gradient decomposition is the central object: Equation (9) splits each deterministic DDIM step into a fixed scaling, a denoising gradient $g_d$, and a likelihood gradient $g_l$. The progressive warm-up inner loop applies $N$ small updates $x_t^{(j+1)} = x_t^{(j)} - (\\zeta/N)\\tilde{g}_l(x_t^{(j)})$ before the denoiser is called, reducing directional conflict with the prior. The ADM recursion $\\tilde{g}_l^{(j)} = \\alpha_j \\beta \\tilde{g}_l^{(j-1)} + (1-\\alpha_j\\beta) g_l^{(j)}$, with $\\alpha_j$ set by the cosine similarity between the momentum and the current gradient, damps temporal fluctuation while remaining responsive to real direction changes. Proposition 4.1 provides the theoretical support: under an $L$-Lipschitz likelihood gradient and step size below $1/L$, the warm-up phase decreases the likelihood objective at every timestep.","core_discovery":"On the paper's own terms, the central discovery is that the reverse process in a Bayesian diffusion solver can be decomposed into a fixed scaling, a denoising gradient $g_d(x_t)$, and a likelihood gradient $g_l(x_t)$, and that the instability of this two-gradient system is a measurable, fixable cause of poor restoration. The paper shows angular measurements of $g_d$ versus $g_l$ deviating from orthogonality in early timesteps and of $g_l$ versus its own previous value swinging widely in intermediate timesteps. SPGD addresses the first with a progressive warm-up: before each DDIM denoising step, it takes $N$ small steps guided only by the smoothed likelihood gradient, so the state already satisfies the measurement constraint when the prior gradient is applied. It addresses the second with adaptive directional momentum, whose effective momentum coefficient $\\alpha_j \\beta$ shrinks when the cosine similarity between the current and accumulated gradient drops. The paper claims these two mechanisms stabilize the whole reverse trajectory and yield state-of-the-art PSNR, SSIM, and LPIPS on FFHQ and ImageNet across four restoration tasks.","pith_inferences":["A stricter control the paper leaves untested is DPS with SPGD's own EDM schedule and $T=100$; without it, part of the reported gap over DPS could be attributed to the schedule rather than to the proposed components.","The same conflict-and-fluctuation diagnosis should transfer to other conditional diffusion settings where a likelihood-like guidance term is added to a denoising gradient—text-to-image, image-to-image translation, video generation—but the paper only lists these as future work.","Proposition 4.1 covers the warm-up without momentum; a descent guarantee for the full ADM version would require bounding the bias introduced by the momentum term, which the paper does not attempt.","A direct mechanism test would correlate per-sample early-conflict angles and fluctuation magnitudes with the gain SPGD delivers over the baseline; the paper's diagnosis predicts larger measured instability corresponds to larger improvement."],"forward_implications":["If the claims hold, SPGD outperforms prior diffusion solvers on FFHQ and ImageNet across inpainting, Gaussian and motion deblurring, and 4x super-resolution, with the largest margins on inpainting and motion deblurring.","SPGD reaches its best results with $T=100$ outer steps and $N=5$ warm-up steps, for 500 function evaluations, and the paper reports it surpasses DPS run for 1,000 steps; trajectory stabilization can substitute for extra sampling compute.","The ablation attributes most of the gain to the warm-up; ADM alone does not help, but in combination it further improves LPIPS, so the two components work synergistically rather than redundantly.","Proposition 4.1 implies the warm-up phase is a descent method on the likelihood objective at each timestep, so the state handed to the denoiser has lower reconstruction error whenever the step-size condition is met."],"supporting_citations":[{"why":"Supplies the DPS likelihood approximation and sampling procedure that SPGD modifies, and is the main baseline to beat.","marker":"[8]"},{"why":"Provides the DDIM deterministic sampling update on which the reverse-step gradient decomposition is built.","marker":"[44]"},{"why":"Supplies the EDM noise schedule and discretization used in SPGD's implementation with T=100.","marker":"[21]"},{"why":"Gives the gradient-view of diffusion sampling that motivates separating the denoising and likelihood gradients.","marker":"[12]"},{"why":"Prior momentum-based diffusion inverse solver whose history-gradient idea ADM adapts into direction-aware form.","marker":"[17]"},{"why":"DiffPIR baseline that SPGD compares against in the restoration experiments.","marker":"[70]"},{"why":"DDRM baseline that SPGD compares against in the restoration experiments.","marker":"[23]"},{"why":"RED-Diff baseline that SPGD compares against in the restoration experiments.","marker":"[29]"}],"fun_headline_variants":["Stabilize diffusion with gradient warm-up and momentum","Gradient management tames diffusion for image restoration","SPGD: smooth gradients for stable diffusion restoration","Warm-up and momentum fix diffusion gradient conflicts","Gradient smoothing boosts diffusion restoration quality"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The measured advantage of SPGD over DPS must come from the warm-up and momentum components, but the paper's ablation 'baseline' uses an improved EDM schedule with $T=100$ while the DPS numbers in Table 1 come from the original DDPM setup with 1,000 steps, and no DPS variant with the same schedule is reported.","fun_headline_variants_meta":{"raw":{"variants":["Stabilize diffusion with gradient warm-up and momentum","Gradient management tames diffusion for image restoration","SPGD: smooth gradients for stable diffusion restoration","Warm-up and momentum fix diffusion gradient conflicts","Gradient smoothing boosts diffusion restoration quality"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000214,"raw_usage":{"total_tokens":1438,"prompt_tokens":969,"completion_tokens":469,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":585,"completion_tokens_details":{"reasoning_tokens":399}},"tokens_in":585,"tokens_out":469,"duration_ms":5420,"temperature":1.0,"reasoning_tokens":399,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T18:57:33.473964+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the original DPS solver under exactly the same conditions as SPGD—EDM schedule, $T=100$ outer steps, one likelihood update per step—on the same 1,000 FFHQ test images, and compare PSNR, SSIM, and LPIPS with full SPGD. If the metrics match or the gap largely disappears, the warm-up and ADM components are not the cause of the improvement; the schedule change is.","supporting_citations":[{"cited_title":"Advances in neural information processing systems 36 (2024)","cited_arxiv_id":null,"evidence_quote":"Supplies the DPS likelihood approximation and sampling procedure that SPGD modifies, and is the main baseline to beat."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the DDIM deterministic sampling update on which the reverse-step gradient decomposition is built."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the gradient-view of diffusion sampling that motivates separating the denoising and likelihood gradients."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior momentum-based diffusion inverse solver whose history-gradient idea ADM adapts into direction-aware form."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"DiffPIR baseline that SPGD compares against in the restoration experiments."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"DDRM baseline that SPGD compares against in the restoration experiments."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"RED-Diff baseline that SPGD compares against in the restoration experiments."}],"review_version":1}