{"id":"0dfbcb7e-dd03-4a9c-862c-5258e0109662","arxiv_id":"2608.08999","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A learnable frequency-domain watermarking scheme for latent diffusion models uses a Slerp-based attack simulation during training and claims lower BER with up to 256-bit payloads.","lead":"DeepFreqMark trains a neural encoder and decoder to embed watermark messages directly into the frequency spectrum of a diffusion model's initial noise latent. It reports lower bit error rates than handcrafted pattern based watermarks and supports messages up to 256 bits.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No shared-protocol BER comparison with baselines; Table III uses metrics from original papers, so the headline claim of lower BER is not yet demonstrated.","rationale":"The reader's conditional verdict identified the Slerp attack proxy as the weak link. I agree that the proxy is under-validated: Table I reports MSE of DDIM inversion under attacks but never shows that a Slerp strength s corresponds to a particular real attack, and the Gaussian-variance claim in Eq. (10) is stated with non-unit vectors. However, the more load-bearing gap is that the paper's headline claim is comparative and no shared-protocol baseline comparison appears anywhere. Table III explicitly uses 'performance metrics reported directly in the original publications,' so the numbers are not comparable: Tree-Rings' 99.50% is verification accuracy, not BER, and RingID, METR, and HSQR accuracies come from different pipelines. This means the central claim could be false even if the Slerp approximation is perfect. The proposed concrete test would settle it. I therefore keep the reader's CONDITIONAL verdict; the paper should be accepted only after the missing shared-protocol comparison is added.","tokens_in":7094,"tokens_out":3861,"duration_ms":34094,"concrete_test":"Run the official implementations of Tree-Rings, RingID, METR, and HSQR under the exact protocol of Table II: same 100 DiffusionDB prompts, same Stable Diffusion v1.5, same eight attacks (cheng2020-anchor3, bmshj2018-factorized3, diff attacker 60, jpeg attacker 50, brightness 0.5, contrast 0.5, Gaussian noise, Gaussian blur), same DDIM inversion, and same BER computation. Compare at a common 32-bit payload and also at each method's native capacity. If DeepFreqMark's average BER is not below every baseline on this shared protocol, the central claim should be revised.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract's central claim is that DeepFreqMark 'achieves significantly lower Bit Error Rates (BER) than baseline methods under real-world attacks.' The experimental section never compares BER with any baseline under a shared protocol. Table II compares only DeepFreqMark's own DCT and FFT variants with and without Slerp training (S=0 vs S=0.6). Table III lists accuracy and capacity numbers attributed to Tree-Rings, RingID, METR, and HSTR/HSQR, but these are taken from the original publications, where attack sets, image sets, message capacities, and evaluation metrics differ (verification accuracy vs. bit accuracy vs. message accuracy). No row reports BER for any baseline on the same 100 prompts, the same eight attacks, the same Stable Diffusion v1.5 pipeline, and the same DDIM-inversion extraction used for DeepFreqMark. Consequently, the comparative claim in the abstract and contribution list is unsupported by the evidence as presented. Even if the Slerp surrogate in Eq. (10) is accepted, the missing head-to-head comparison remains. A secondary concern is that Eq. (10) as written uses non-unit vectors while claiming to preserve Gaussian variance; this deserves clarification, but it is secondary to the absent baseline comparison.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes DeepFreqMark, an end-to-end learnable frequency-domain watermarking framework for latent diffusion models. A neural encoder embeds binary messages into the DCT or FFT spectrum of the initial noise latent, and a neural decoder recovers the message after DDIM inversion. To avoid the computational cost of DDIM inversion during training, the authors introduce a Slerp-based attack simulation that perturbs the noise latent directly, with a training objective combining latent reconstruction MSE and binary cross-entropy for message recovery. Experiments with Stable Diffusion v1.5 report BER for DCT and FFT variants with and without Slerp training, and accuracy/capacity comparisons with Tree-Rings, RingID, METR, and HSTR/HSQR.","tokens_in":7385,"tokens_out":4282,"duration_ms":38835,"significance":"If the robustness and capacity claims were substantiated, this would be a useful contribution: it replaces handcrafted frequency patterns with a learned encoder/decoder, extends embedding to DCT as well as FFT, handles Hermitian symmetry properly, and scales to 256-bit payloads. The release of source code is a strength, and the idea of avoiding DDIM inversion during training via a latent-space surrogate is practically motivated. However, the headline BER claim is not currently supported by a shared-protocol comparison, and the Slerp surrogate's validity is not established, so the significance cannot be fully assessed.","major_comments":[{"comment":"The central claim in the abstract and Section I that DeepFreqMark 'achieves significantly lower Bit Error Rates (BER) than baseline methods' is not supported by the experiments as presented. Table II compares only DeepFreqMark's own DCT and FFT variants with S=0 and S=0.6; no baseline method is evaluated under the same protocol (same 100 DiffusionDB prompts, same Stable Diffusion v1.5 pipeline, same eight attacks, same DDIM-inversion extraction). Table III lists accuracy and capacity values taken from the original publications, where attack sets, image sets, message capacities, and metrics (verification accuracy vs. bit accuracy) differ, and no BER row is reported for any baseline. A head-to-head BER comparison on a shared protocol is needed to substantiate the comparative claim.","section":"IV.B (Tables II and III)"},{"comment":"The Slerp-based attack simulation is a load-bearing ingredient, but the paper does not validate that Slerp on the noise latent approximates the effect of real image-level attacks after DDIM inversion. Table I reports only MSE values of DDIM-inverted latents under several attacks; it does not map a Slerp strength s to any real attack, nor does it show that models trained with S=0.6 transfer to actual DDIM-inversion attacks better than models trained without Slerp. Without such validation, the robustness improvements in Table II may reflect overfitting to the Slerp distribution rather than generalization to real-world attacks. I recommend adding a transfer experiment that compares Slerp-trained and non-Slerp-trained models under the Table I attacks, and ideally a calibration of s against attack MSE.","section":"III.D and Table I"},{"comment":"Eq. (10) writes Slerp(z'_T, z_r, s) with the standard formula for unit vectors, but z'_T and z_r are Gaussian noise latents that are not normalized in general. Applied to vectors of different norms, this formula does not preserve the norm, and the claimed 'unit variance and underlying Gaussian profile' guarantee is not justified. The authors should either define Slerp on normalized vectors and state the variance-preservation argument explicitly, or provide an alternative formula; as written, this is a technical error in the core simulation.","section":"III.D, Eq. (10)"}],"minor_comments":[{"comment":"The notation moves between Z'_T (frequency domain) and z'_T (spatial latent) without defining the inverse transform; please clarify which domain each loss operates in.","section":"III.B, Eqs. (1)-(3)"},{"comment":"The 'Accuracy' column mixes verification accuracy, bit accuracy, and message accuracy across methods; please define the metric for each row or use a single shared metric for all rows.","section":"Table III"},{"comment":"No confidence intervals or number of test samples are reported; please add error bars or state the sample size at each point.","section":"Figures 7-9"},{"comment":"The caption says the gap between |m|=128 and |m|=256 is shortened for better visualization, but the axis appears discontinuous; please make the axis transformation explicit or plot the true scale.","section":"Figure 9"},{"comment":"Minor typos: Section IV.F heading has an extra space ('F . Superiority'), and Table I columns are labeled 'MSE Error' though MSE is already an error measure.","section":"Section IV.F and Table I"}],"recommendation":"major_revision","confidential_remarks":"The strongest aspect is the learnable frequency-domain framework, and the missing shared-protocol comparison and unvalidated Slerp surrogate are fixable in a revision; I do not see grounds for rejection. No apparent novelty-disclosure issue."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"I read DeepFreqMark with interest. The core idea is a real departure from the handcrafted-ring watermarks in this space: a small CNN encodes a binary message into a DCT or FFT patch of the initial noise latent, and a matching decoder recovers the message after DDIM inversion and image attacks. Training the encoder/decoder with a Slerp-based perturbation of the latent, instead of running DDIM inversion at every step, is a clever way to make robustness training feasible. The paper also releases code, which helps reproducibility. On its own ablation, the Slerp training (S=0.6) clearly lowers BER compared with no attack simulation, across both DCT and FFT variants, on the eight attacks tested. That is a meaningful empirical result.\n\nWhere the paper falls short is in supporting the abstract's claim that DeepFreqMark \"achieves significantly lower Bit Error Rates than baseline methods under real-world attacks.\" Table II compares only the method's own variants. Table III compares accuracy and capacity values taken directly from the original Tree-Rings, RingID, METR, and HSTR/HSQR papers, which used different attack sets, different image sets, different message lengths, and different metrics (verification accuracy vs. bit accuracy). There is no baseline BER measured on the same 100 prompts, the same eight attacks, and the same Stable Diffusion pipeline. Without that shared-protocol comparison, the superiority claim is not demonstrated.\n\nThe Slerp surrogate itself is also under-validated. The paper reports MSE of DDIM-inverted latents under various attacks (Table I), but never shows that a Slerp step of some strength resembles those inverted latents, nor that training with Slerp transfers to real inversion. That is a fixable gap, but it is load-bearing.\n\nOne mathematical point needs attention: Eq. (10) is written as the standard Slerp formula for unit-norm vectors, while z'_T and z_r are not unit vectors (z'_T is a watermarked latent that differs slightly from a Gaussian draw, and z_r is sampled from N(0,I)). The claim that Slerp \"strictly preserves\" Gaussian variance is therefore not obviously true as written. The authors should either normalize the vectors first or clarify why the variance is preserved despite non-unit inputs.\n\nWho is this for? Readers working on generative-model provenance and diffusion watermarking will find the learned embedding and the Slerp idea worth engaging with. The paper deserves a serious referee and revision; I would not reject it outright. But I would send it back with requests for a shared baseline protocol, a direct validation of the Slerp surrogate, and a corrected or clarified Eq. (10).","headline":"DeepFreqMark introduces a genuinely learnable frequency-domain watermark and a Slerp attack surrogate, but the claimed superiority over baselines is not yet supported by a shared-protocol comparison.","tokens_in":7859,"tokens_out":3446,"would_cite":false,"duration_ms":30478,"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":"DeepFreqMark replaces handcrafted frequency watermarks with a learned encoder-decoder and a Slerp-based attack simulation to lower bit-error rates and scale payloads to 256 bits.","keywords":["latent diffusion model watermarking","learnable frequency-domain embedding","Slerp attack simulation","DDIM inversion","message capacity","FFT watermarking","DCT watermarking","generative image provenance"],"falsifier":"Evaluate a Slerp-trained model and a non-Slerp model under the actual DDIM-inversion pipeline with the attacks in Table I; if the Slerp-trained model does not show clearly lower BER on those real attacks, or if the BER-versus-$S$ trend in Fig. 7 does not match the MSE ranking in Table I, the surrogate-attack assumption is falsified.","tokens_in":6815,"feed_emoji":"🔐","tokens_out":8716,"duration_ms":76103,"temperature":0.7,"pith_summary":"DeepFreqMark aims to establish that watermarking images from latent diffusion models can be done with a learned neural encoder and decoder rather than fixed geometric patterns. It writes a binary message into a low-frequency patch of the initial noise spectrum, and it reads the message back from the DDIM-inverted noise of the generated image. Because running DDIM inversion during every training step is too expensive, the paper introduces a spherical-interpolation (Slerp) attack simulation that nudges the watermarked noise toward a random Gaussian noise while preserving its variance, as a cheap surrogate for real image attacks. The reported experiments support the claim that this approach lowers bit-error rates under attacks such as JPEG, blur, noise, brightness and learned compression, and that it scales the payload to 256 bits, far beyond what the compared ring-based methods achieve.","feed_headline":"Learned watermarks beat handcrafted rings in diffusion images","feed_subtitle":"A neural encoder in the noise spectrum cuts bit errors below one percent while carrying 256-bit messages.","key_machinery":"The load-bearing mechanism is the Slerp-based attack simulation (Equation 10) applied to the noise latent during training. Spherical linear interpolation moves the watermarked latent $z'_T$ along the great-circle arc toward a random Gaussian vector $z_r$, with strength $s\\sim U(0,S)$; because both endpoints lie on the Gaussian annulus, the interpolated latent stays on the high-dimensional sphere and preserves unit variance, avoiding the variance collapse that ordinary linear interpolation would cause. This surrogate stands in for the expensive sequence of image-level attack plus DDIM inversion, letting the encoder and decoder be optimized for robustness in each training step. The second supporting mechanism is the frequency-patch embedding: the encoder outputs a real watermark for DCT and a two-channel complex watermark for FFT, with the FFT scheme enforcing Hermitian symmetry via $F[M-k,N-l]=F[k,l]$ on a free half-region, ensuring the inverse transform is real-valued.","core_discovery":"The paper's central claim is that a learnable end-to-end encoder/decoder operating in the frequency domain of the initial noise latent can outperform handcrafted frequency-domain watermarks for latent diffusion models, and that the key enabler is a Slerp-based surrogate attack. The message encoder maps a binary message to a small $32\\times32$ patch in the DCT or FFT spectrum of the last channel of the noise latent; the FFT variant uses a free half-region and Hermitian symmetry to guarantee real-valued latents. During extraction, the attacked image is mapped back by DDIM inversion, cropped in the same frequency patch, and decoded. Against real-world attacks such as JPEG, Gaussian noise/blur, brightness/contrast, and neural re-compression, the FFT model trained with Slerp strength $S=0.6$ reports an average BER of $0.316\\%$ versus $1.976\\%$ without simulation, and the same setup reports $99.44\\%$ bit accuracy at 256-bit payloads. These numbers constitute the paper's evidence that the Slerp proxy transfers to real DDIM-inversion-based decoding.","pith_inferences":["Editorial extension: the Slerp-to-real-attack mapping is not directly validated; a natural test is to calibrate the sampled $s$ against Table I's DDIM-inversion MSEs, and if no single $s$ covers all attack severities, training should sample a mixture of strengths rather than a uniform $U(0,S)$.","Editorial extension: if the Slerp proxy transfers faithfully, the same latent-interpolation trick could be applied to other generative models whose inversion is deterministic, not only DDIM-based diffusion.","Editorial extension: the FFT variant's consistent edge suggests that the complex phase carries much of the robust signal; perturbing phase while holding magnitude fixed would reveal whether the decoder truly exploits phase or simply the Hermitian redundancy."],"forward_implications":["The training cost of attack-aware watermarking can drop sharply, because the Slerp surrogate replaces the DDIM inversion loop that would otherwise run at every iteration.","Payload capacity for in-generation watermarks jumps from 11–72 bits in the compared handcrafted schemes to 256 bits while keeping reported bit accuracy above 99%, which makes per-user message assignment practical.","The same learnable recipe works in both DCT and FFT domains, with the FFT variant consistently more robust, indicating that the method generalizes across spectral representations.","Average BER below roughly 0.5% leaves room for standard error-correcting codes, so near-zero-error provenance tracking is within reach for the tested attack suite.","Raising the Slerp strength lowers BER but visibly degrades image quality once $S\\ge 0.8$, giving a tunable robustness-versus-fidelity dial for deployment."],"supporting_citations":[{"why":"Supplies the latent diffusion model (Stable Diffusion) that the watermarking pipeline operates on and that is used for generation in the experiments.","marker":"[1]"},{"why":"Introduces the Tree-Rings handcrafted FFT watermark, the low-capacity baseline DeepFreqMark compares against and improves upon.","marker":"[4]"},{"why":"METR encodes bits into rings and provides the 16-bit capacity/accuracy comparison point for the claimed capacity scaling.","marker":"[5]"},{"why":"RingID is the multi-key identification baseline whose accuracy and 11-bit payload are used in the comparison table.","marker":"[6]"},{"why":"HSTR/HSQR supplies the Hermitian-symmetric frequency design and the 72-bit baseline that motivates DeepFreqMark's FFT free half-region.","marker":"[7]"},{"why":"DDIM inversion is the deterministic image-to-noise mapping that makes the embedding readable and defines the extraction pipeline.","marker":"[8]"},{"why":"Provides the cheng2020-anchor learned image compression attack used as one of the real-world robustness tests.","marker":"[9]"},{"why":"Provides the bmshj2018-factorized learned compression attack used in the BER evaluation.","marker":"[10]"},{"why":"Supplies the diffusion-based purification attack (diff attacker 60) that the watermarks must survive.","marker":"[11]"},{"why":"Supplies the DiffusionDB prompt set used to sample the 100 text prompts for the robustness experiments.","marker":"[12]"}],"fun_headline_variants":["Neural watermarking outsmarts diffusion image attacks","Learnable frequency watermarks slash bit errors in diffusion","DeepFreqMark: AI watermarking with Slerp attack training","Diffusion watermarking goes neural with 256-bit capacity","End-to-end frequency watermarking beats handcrafted patterns"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The robustness gain rests on the unproven premise that moving the watermarked noise partway toward a random Gaussian noise during training mimics what real image attacks do to the latent after DDIM inversion, so if that proxy is wrong the reported low bit-error rates may not appear outside the training setup.","fun_headline_variants_meta":{"raw":{"variants":["Neural watermarking outsmarts diffusion image attacks","Learnable frequency watermarks slash bit errors in diffusion","DeepFreqMark: AI watermarking with Slerp attack training","Diffusion watermarking goes neural with 256-bit capacity","End-to-end frequency watermarking beats handcrafted patterns"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000222,"raw_usage":{"total_tokens":1460,"prompt_tokens":960,"completion_tokens":500,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":576,"completion_tokens_details":{"reasoning_tokens":418}},"tokens_in":576,"tokens_out":500,"duration_ms":4482,"temperature":1.0,"reasoning_tokens":418,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:17:21.121719+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Evaluate a Slerp-trained model and a non-Slerp model under the actual DDIM-inversion pipeline with the attacks in Table I; if the Slerp-trained model does not show clearly lower BER on those real attacks, or if the BER-versus-$S$ trend in Fig. 7 does not match the MSE ranking in Table I, the surrogate-attack assumption is falsified.","supporting_citations":[{"cited_title":"High-resolution image synthesis with latent diffusion models,","cited_arxiv_id":null,"evidence_quote":"Supplies the latent diffusion model (Stable Diffusion) that the watermarking pipeline operates on and that is used for generation in the experiments."},{"cited_title":"METR: Image Watermarking with Large Number of Unique Messages","cited_arxiv_id":"2408.08340","evidence_quote":"METR encodes bits into rings and provides the 16-bit capacity/accuracy comparison point for the claimed capacity scaling."},{"cited_title":"Ringid: Rethinking tree-ring watermarking for enhanced multi- key identification,","cited_arxiv_id":null,"evidence_quote":"RingID is the multi-key identification baseline whose accuracy and 11-bit payload are used in the comparison table."},{"cited_title":"Semantic watermarking reinvented: Enhancing robustness and generation quality with fourier integrity,","cited_arxiv_id":null,"evidence_quote":"HSTR/HSQR supplies the Hermitian-symmetric frequency design and the 72-bit baseline that motivates DeepFreqMark's FFT free half-region."},{"cited_title":"Learned image compression with discretized gaussian mixture likelihoods and attention modules,","cited_arxiv_id":null,"evidence_quote":"Provides the cheng2020-anchor learned image compression attack used as one of the real-world robustness tests."},{"cited_title":"Invisible image watermarks are provably removable using generative ai,","cited_arxiv_id":null,"evidence_quote":"Supplies the diffusion-based purification attack (diff attacker 60) that the watermarks must survive."}],"review_version":1}