{"id":"3bf51577-c643-40da-83ad-07e5dd5cf70d","arxiv_id":"2511.00870","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A multi-GPU Plug-and-Play MCMC sampler with CNN denoisers reconstructs 4096×4096 color images while giving pixel-wise uncertainty maps.","lead":"This paper shows how to run a Bayesian image-reconstruction algorithm on several graphics cards at once by splitting the image into blocks and exchanging only a thin strip of pixels between neighboring blocks. It tests the approach on images up to 4096×4096 pixels and reports speed-ups when the denoiser is expensive enough relative to communication.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The machine-precision equivalence claim rests on an unproven block-separability assertion (A5) for the CNN-induced prior; any boundary mismatch in the distributed denoiser would make Algorithm 1 target a different posterior for B>1.","rationale":"The reader's weakest assumption is exactly the unproven block-separability (A5) of the CNN-induced prior, and my independent reading identifies the same point as the most load-bearing. The central claim—that the distributed sampler is numerically equivalent to its serial counterpart—depends on the distributed evaluation of D_epsilon being identical to the serial network. The paper asserts this via A5 but gives neither a proof nor empirical evidence. Without this equivalence, the distributed PnP-ULA transition is not the serial PnP-ULA transition, so the sampler may target a different posterior when B>1. This is a correctness risk, not merely a missing baseline or stylistic issue. The concrete test I propose directly checks the equivalence claim by comparing trajectories and denoiser outputs at machine precision; it would settle whether the concern is substantive or whether the implementation is indeed exact. I agree with the reader's CONDITIONAL verdict, so no change is recommended.","tokens_in":19994,"tokens_out":10652,"duration_ms":129268,"concrete_test":"Release the code and run a controlled equivalence check. Use a fixed seed and generate Gaussian increments xi^(t) once serially; for B=4, feed each worker the corresponding subvector. Run Algorithm 1 on the inpainting task (Section III-A1) with DDFB (K=4) and DRUNet for T=100 iterations, and compute max_t ||x^(t)_{B=4} − x^(t)_{B=1}||_inf. Separately, for 100 random images, compare the full D_epsilon output computed by the distributed overlap-save code against the serial network, and report the maximum absolute difference in the overlap regions. If either difference exceeds 1e-12, the equivalence claim (and A5) fails; if both are at machine precision, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is numerical equivalence between the distributed sampler and serial PnP-ULA: Section IV-B states that 'operation outputs coincide for any number of workers B down to machine precision.' The only justification offered is the assertion in Section II-C that, after distributing D_epsilon with overlap-save, 'the associated prior p satisfies Assumption (A5)'—i.e., log p is block-additively separable as in Eq. (6). No proof or empirical verification is given. The concern is not merely formal: the distributed convolution in Eq. (19)–(20) uses an extended block of size eN_{y,b}=N_{y,b}+L_y−1 (Eq. 18), i.e., a one-sided ghost region. For a symmetric convolution kernel, output rows at the top of block b depend on input rows in block b−1, which this extension does not include. If the local convolution W_{k,b} applies zero padding at that interface instead of receiving the missing halo, the distributed D_epsilon differs from the serial network at every block boundary. Then the induced prior is not of the form (6) with local S_{0,b}, and Algorithm 1 lines 9–11 implement a different transition kernel than serial PnP-ULA. The machine-precision equivalence, and the scalability conclusions built on it, are therefore unsupported. The assertion in Section IV-B that estimates are identical for B in {1,2,4} is stated without any numerical comparison or released code, so the reader cannot check whether the distributed denoiser actually reproduces the serial network at block boundaries.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a distributed MCMC sampler for high-dimensional Bayesian imaging inverse problems. It combines the split Gibbs / approximate data augmentation (AXDA) framework with Plug-and-Play unadjusted Langevin algorithm (PnP-ULA), and distributes all operators—including convolutional neural network denoisers—over multiple GPUs using an SPMD architecture. The central claims are (i) the distributed sampler is numerically equivalent to its serial counterpart, producing identical outputs for B=1,2,4 workers down to machine precision (Sec. IV-B); (ii) it scales to images as large as 4096^2 color images (Sec. IV-C); and (iii) reconstruction quality is 'comparable to other PnP methods' despite the distributed implementation. The paper reports communication and computation overheads for three denoiser architectures (DDFB, DnCNN, DRUNet) and gives strong/weak scaling experiments on inpainting and deconvolution under Gaussian and Poisson noise.","tokens_in":20405,"tokens_out":4248,"duration_ms":52526,"significance":"If the central equivalence claim is correct, this is a practically valuable contribution: it would be the first distributed PnP-MCMC scheme that retains the statistical guarantees of serial PnP-ULA while scaling to very high resolution. The paper has genuine engineering strengths: the communication-aware treatment of CNN layers (overlap-save with ghost regions, Eqs. (19)-(20)), the detailed FLOP/message-size analysis in Table IV, and the scalability experiments on a real multi-GPU system (Tables VI-VII) are nontrivial and useful. The authors also make a good faith effort to compare three different CNN priors and a TV baseline. However, the load-bearing claim of machine-precision equivalence rests on an unproven structural assumption about the denoiser-induced prior, and the experimental support for the 'comparable to other PnP methods' statement is currently limited to a comparison with a TV baseline, not with other PnP methods or even serial PnP-ULA. These gaps need to be addressed before the central claims can be accepted.","major_comments":[{"comment":"The paper asserts that after distributing D_epsilon with the overlap-save strategy of Section II-B2, 'the associated prior p satisfies Assumption (A5)' (block-additive separability of log p with respect to the same partition as the operators). This is the key step that allows Algorithm 1 to be interpreted as a distributed implementation of serial PnP-ULA. No proof is provided, and the assertion is not obvious. For a PnP prior defined through a denoiser, log p is not explicitly known; even if each convolution layer is local with a halo, the composition of convolutions, nonlinearities, and (for DRUNet) down/up-sampling does not automatically yield a log-density that is exactly block-additive in the sense of Eq. (6). Moreover, the halo defined in Eq. (18) is one-sided (eB_b extends only in the +Ny direction by L_y-1). For a symmetric convolution kernel, computing output rows at the top of b","section":"Section II-C, after Eq. (25); Assumption (A5), Eq. (6)"},{"comment":"The statement that 'Algorithm 1 produces estimates of the same quality for B in {1,2,4}. In particular, operation outputs coincide for any number of workers B down to machine precision, except the generation of pseudo-random numbers' is central to the paper's contribution, but it is not supported by any reported numerical comparison. Table V reports a single value per metric and prior, with no indication of how the B=1,2,4 runs were aggregated, no standard deviations, and no repeated-seed variability. There is also no release of the code or data (the link in Section III is a placeholder 'https://repo/to/code'), so the reader cannot reproduce or verify the equivalence claim. In addition, the abstract's 'reconstruction performance comparable to other PnP methods' is not tested: the experiments compare the proposed sampler with a TV baseline and with three denoiser choices, but there is no","section":"Section IV-B, Table V and text near 'operation outputs coincide'"},{"comment":"The authors themselves note that DRUNet 'performance deteriorates sharply' in Poisson deconvolution and that the poor results 'suggest instability during sampling, likely caused by an underestimation of L_D'. This is an acknowledged limitation, but it interacts with the paper's broad claim that the sampler achieves performance 'comparable to other PnP methods'. If the estimated Lipschitz constant is unreliable for a state-of-the-art denoiser such as DRUNet, the practical utility of the method for general CNNs is diminished. The authors should either (i) provide a more careful Lipschitz estimation procedure (e.g., spectral normalization or power iteration) and rerun the affected experiments, or (ii) clearly delimit the claim to the architectures for which the sampler is stable (here, DDFB appears to be the only consistently stable learned prior). The current text leaves the reader uncerta","section":"Section IV-B, DRUNet discussion"}],"minor_comments":[{"comment":"The code URL is a placeholder ('https://repo/to/code'). If the paper is intended for publication, a working repository should be provided or the statement should be removed.","section":"Section III, code availability"},{"comment":"Table V reports metrics for B in {1,2,4} but the table has no B dimension. Please clarify whether the values are identical across B by construction, or report them separately. If the equivalence claim is established, a sentence stating that values are identical to machine precision would be sufficient.","section":"Table V"},{"comment":"Typo: 'auxilliary' should be 'auxiliary'.","section":"Section II-C, second paragraph"},{"comment":"The notation for the extended block is slightly confusing: eB_b is defined as a set of indices, but later eNy,b is used for its cardinality. Please make the distinction between the set and its size explicit.","section":"Section II-B2a, Eq. (18)"},{"comment":"Formatting issue in the reference: 'F oundations' should be 'Foundations'.","section":"Reference [34]"}],"recommendation":"major_revision","confidential_remarks":"The paper is a reasonable engineering contribution, but the refereeing process should verify the block-separability assumption (A5) before publication. The claim of machine-precision equivalence is the hook of the paper, and it is currently supported only by an unproven assertion. Adding a small numerical experiment comparing distributed and serial denoisers (and, if possible, the full samplers) would considerably strengthen the paper. I also recommend that the editor ask the authors to clarify the scope of the 'comparable to other PnP methods' statement, since the current experiments do not include any other PnP-MCMC baseline."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing here is the distributed evaluation of general CNN denoisers inside a PnP-ULA/Split-Gibbs sampler, using ghost regions and overlap-save, plus the communication-cost comparison across DDFB, DnCNN, and DRUNet. That is a real extension beyond the earlier TV-only distributed sampler and the preliminary DDFB results, and the scaling experiments up to 4096^2 color images are substantial. The paper is clearly written, and the authors are honest about DRUNet instability under Poisson noise, which I appreciate.\n\nThe main soft spot is the theoretical gap around Assumption (A5). The paper simply asserts that the CNN-induced prior is block-additively separable after the distributed denoiser, and on that basis claims the distributed sampler is numerically equivalent to serial PnP-ULA down to machine precision. No proof or empirical verification is provided, and the code is a placeholder, so the reader cannot check. The stress-test note about the one-sided ghost region in Eq. (18)–(20) is a concrete version of this worry: for a symmetric kernel, output rows at the top of a block need input rows from the previous block, which the extension does not include. I don't know without running the code whether the implementation actually handles this (the reversal of communication direction between layers might be part of the story), but the burden is on the authors to demonstrate it. This is not a fatal flaw in the overall idea, but it is load-bearing for the central equivalence claim.\n\nTwo smaller issues. First, the abstract says reconstruction performance is 'comparable to other PnP methods,' but the experiments only compare against a TV baseline and different denoisers within their own sampler — there is no comparison to other PnP algorithms. Second, the quality metrics in Table V have no error bars or repeated-seed variability; for MCMC, that matters.\n\nOverall, this is a solid engineering contribution that deserves a serious referee. The distributed communication analysis is useful, and the scaling results are credible, but the paper needs revision: release the code, prove or empirically validate the (A5) equivalence, add baselines and error bars. If those are addressed, it would be a good addition to the imaging inverse-problems literature.","headline":"Useful distributed PnP-ULA extension with real scaling results, but the machine-precision equivalence claim rests on an unproven block-separability assumption and there is no code.","tokens_in":20891,"tokens_out":6554,"would_cite":true,"duration_ms":70989,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62F15","65C05","68U10"],"pacs":[],"model":"deepseek-v4-flash","headline":"A distributed plug-and-play MCMC sampler scales Bayesian image reconstruction to 4096^2 color images on multiple GPUs while preserving the exact posterior of the serial run.","keywords":["MCMC","plug-and-play priors","Langevin algorithms","distributed computing","imaging inverse problems","uncertainty quantification","convolutional neural networks","split Gibbs sampler"],"falsifier":"Take a trained CNN denoiser, compute (or estimate by finite differences) the score function of the prior it induces—for instance via the Tweedie relation—and check whether log p(x) separates as the sum of per-block terms on a 2-worker partition; a single partition where separability fails would falsify the core equivalence. Alternatively, compare serial and distributed chains on the same problem with many random seeds and test whether the empirical distributions of the samples agree beyond machine-precision arithmetic.","tokens_in":19887,"feed_emoji":"🖼️","tokens_out":6104,"duration_ms":61345,"temperature":0.7,"pith_summary":"This paper argues that plug-and-play MCMC imaging—Bayesian inversion with a neural-network denoiser as prior—can be made to scale to very large images by distributing every operator, including the denoiser, across multiple workers. The proposed sampler splits the posterior into local blocks using an augmented auxiliary variable, applies a Langevin update with a CNN denoiser, and coordinates workers with small boundary exchanges. The central claim is that the distributed sampler reproduces the serial sampler's outputs to machine precision for any number of workers, while running fast enough to handle 4096^2 color images with pixel-wise uncertainty maps. If true, it removes the memory and runtime barriers that currently confine plug-and-play MCMC to moderate-size problems.","feed_headline":"Distributed MCMC sampler scales Bayesian imaging to 4096^2 pixels","feed_subtitle":"Multi-GPU runs keep the serial posterior, bringing Bayesian uncertainty maps to 4096^2-color images.","key_machinery":"The load-bearing mechanism is the localized-operator decomposition: linear operators such as convolutions are expressed as blocks that depend only on local selections of the input plus small 'ghost' regions exchanged between neighboring workers. For the CNN denoiser, each convolutional layer is distributed with an overlap-save scheme, so the network evaluates on each worker up to boundary communication. The associated log-prior is assumed block-additively separable with respect to the same partition (Assumption A5); this is what lets the PnP-ULA update (Eq. 24) and PSGLA auxiliary update (Eq. 25) factor across workers without changing the target distribution.","core_discovery":"The paper's central discovery is that a PnP-ULA transition and its auxiliary-variable Gibbs step can be implemented in a distributed SPMD fashion with a localized CNN denoiser, so that the posterior remains unchanged. Concretely, Algorithm 1 decomposes the gradient of the data-fidelity term, the proximal map of the regularizer, and the denoiser itself via overlap-save convolutions and ghost-region communications; under block-additive separability of the log-prior, each worker updates its own slice of x and z. The authors report that for B in {1,2,4} the operation outputs coincide down to machine precision (modulo random-number generation), and that the sampler enables sampling of 4096^2 colo","pith_inferences":["Editorial extension: the block-separability of the denoiser-induced prior (Assumption A5) is asserted rather than proved; a denoiser with a global receptive field or one whose boundary handling couples blocks would break the machine-precision equivalence, so the claim is only as strong as that separability.","Editorial extension: a direct test of the equivalence claim is to compare serial and distributed chains under several random seeds; since only pseudo-random generation differs, statistical agreement rather than bitwise agreement is the appropriate criterion.","Editorial extension: the overlap-save distribution strategy suggests a recipe for scaling other plug-and-play samplers, such as diffusion-based priors, provided their non-local operations can be localized; communicating the full receptive field across layers is a costly alternative the paper explicitly leaves open.","Editorial extension: the scaling results imply the method pays off when per-worker compute dominates communication; for cheap priors like total variation, distribution can slow the sampler, so the practical benefit is conditional on network cost."],"forward_implications":["Plug-and-play MCMC can be applied to images at 4096^2 pixels, producing MMSE estimates and pixel-wise variance maps that a single-GPU sampler cannot fit in memory.","Users can increase the number of workers without re-tuning the sampler: because the distributed and serial outputs coincide to machine precision, the target posterior is the same for any B.","Lightweight CNNs with few layers become attractive for distributed sampling: they preserve reconstruction quality while keeping communication phases and message sizes small.","The same distributed treatment extends naturally to other inverse problems where the observation operator is local, covering common Gaussian and Poisson imaging models."],"fun_headline_variants":["Distributed MCMC hits 4096^2 Bayesian imaging","Multi-GPU MCMC: full posterior at 16M pixels","PnP-ULA scales to 4096^2 with unchanged posterior","Distributed sampler brings Bayesian UQ to 4096^2","Overlap-save denoiser enables distributed PnP-MCMC"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The whole equivalence rests on the assertion, stated without proof or empirical check in Section II-C, that the prior density induced by the distributed CNN denoiser is block-additively separable with respect to the same partition as the observation operators; if that separability fails, Algorithm 1 samples a different posterior than the serial PnP-ULA.","fun_headline_variants_meta":{"raw":{"variants":["Distributed MCMC hits 4096^2 Bayesian imaging","Multi-GPU MCMC: full posterior at 16M pixels","PnP-ULA scales to 4096^2 with unchanged posterior","Distributed sampler brings Bayesian UQ to 4096^2","Overlap-save denoiser enables distributed PnP-MCMC"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000213,"raw_usage":{"total_tokens":1254,"prompt_tokens":734,"completion_tokens":520,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":478,"completion_tokens_details":{"reasoning_tokens":428}},"tokens_in":478,"tokens_out":520,"duration_ms":5898,"temperature":1.0,"reasoning_tokens":428,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T00:24:44.775210+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a trained CNN denoiser, compute (or estimate by finite differences) the score function of the prior it induces—for instance via the Tweedie relation—and check whether log p(x) separates as the sum of per-block terms on a 2-worker partition; a single partition where separability fails would falsify the core equivalence. Alternatively, compare serial and distributed chains on the same problem with many random seeds and test whether the empirical distributions of the samples agree beyond machine-precision arithmetic.","supporting_citations":[],"review_version":1}