Title: DiffBreak: Is Diffusion-Based Purification Robust?
Venue: NeurIPS 2025
Accepted: yes
Keywords: Adaptive Adversarial Attacks

Adversarial Purification

Diffusion Models
Abstract: Diffusion-based purification (DBP) has become a cornerstone defense against adversarial examples (AEs), regarded as robust due to its use of diffusion models (DMs) that project AEs onto the natural data manifold. We refute this core claim, theoretically proving that gradient-based attacks effectively target the DM rather than the classifier, causing DBP's outputs to align with adversarial distributions. This prompts a reassessment of DBP's robustness, accrediting it two critical factors: inaccurate gradients and improper evaluation protocols that test only a single random purification of the AE. We show that when accounting for stochasticity and resubmission risk, DBP collapses. To support this, we introduce DiffBreak, the first reliable toolkit for differentiation through DBP, eliminating gradient mismatches that previously further inflated robustness estimates. We also analyze the current defense scheme used for DBP where classification relies on a single purification, pinpointing its inherent invalidity. We provide a statistically grounded majority-vote (MV) alternative that aggregates predictions across multiple purified copies, showing partial but meaningful robustness gain. We then propose a novel adaptation of an optimization method against deepfake watermarking, crafting systemic perturbations that defeat DBP even under MV, challenging DBP's viability.

DiffBreak: Is Diffusion-Based Purification Robust?

Abstract

Diffusion-based purification ( DBP ) has become a cornerstone defense against adversarial examples ( AE s), regarded as robust due to its use of diffusion models ( DM s) that project AE s onto the natural data manifold. We refute this core claim, theoretically proving that gradient-based attacks effectively target the DM rather than the classifier, causing DBP 's outputs to align with adversarial distributions. This prompts a reassessment of DBP 's robustness, accrediting it two critical factors: inaccurate gradients and improper evaluation protocols that test only a single random purification of the AE . We show that when accounting for stochasticity and resubmission risk, DBP collapses. To support this, we introduce DiffBreak , the first reliable toolkit for differentiation through DBP , eliminating gradient mismatches that previously further inflated robustness estimates. We also analyze the current defense scheme used for DBP where classification relies on a single purification, pinpointing its inherent invalidity. We provide a statistically grounded majorityvote ( MV ) alternative that aggregates predictions across multiple purified copies, showing partial but meaningful robustness gain. We then propose a novel adaptation of an optimization method against deepfake watermarking, crafting systemic perturbations that defeat DBP even under MV , challenging DBP 's viability.

1 Introduction

ML classifiers are vulnerable to Adversarial Examples (AEs) -imperceptible perturbations that induce misclassification [37, 15]. Adversarial Training [28, 54] is attack-specific and costly [44], while other defenses [16, 13, 3, 46, 49, 32, 50, 9] are vulnerable to adaptive attacks [38]. Diffusion-Based Purification (DBP) [30, 40], which leverages diffusion models (DMs) [36, 34], has emerged as a promising defense [6, 45, 7, 53, 31, 42]. DBP purifies inputs by solving the reverse stochastic differential equation ( SDE ) associated with DM s, diffusing the input with random noise to dilute adversarial changes and iteratively denoising it. Given DMs' data modeling abilities [12, 39], DBP operates under the assumption that each denoising (reverse) step's output belongs to a corresponding marginal natural distribution (a distribution obtained by introducing Gaussian noise into natural inputs, with decreasing variance proportional to that step).

This is the foundation for DBP 's robustness as it ensures its outputs are from the natural distribution, while AE s lie outside this manifold and are unlikely to be preserved. Recent works treat DBP as a static pre-processor that standard gradient-based attacks cannot directly manipulate but rather only attempt to evade. Thus, attackers are assumed to either fail due to randomness that masks the classifier's vulnerabilities [26], or be forced to rely on surrogate losses and heuristic approximations [20, 41]. We theoretically refute DBP 's robustness rooted in its ability to perform projection onto the natural manifold. This is paradoxical as it assumes correct behavior of the score model s θ used by the DM to mimic the gradients of the marginal distributions. Yet, s θ is an ML system with exploitable imperfections. In §3.1, we prove that standard adaptive attacks that simply backpropagate the classifier's loss gradients through DBP effectively target s θ rather than the classifier , forcing it to generate samples from an adversarial distribution. Hence, DBP 's theory no longer holds.

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In §3.2 and §3.3, we revisit DBP 's previous robustness, attributing it to backpropagation issues and improper evaluation protocols. Most works [20, 30, 26, 40] judge attacks based on a single purification of the final adversarial input. While this seemingly mirrors DBP 's intended 'purify once and classify' deployment [30, 40], it is statistically invalid: since DBP samples noise randomly, one evaluation of the AE fails to capture true single misclassification probability across possible purifications. Moreover, due to DBP 's memory-intensive gradients, prior works implement exact backpropagation [20, 26, 41] via checkpointing [8]. We discover and fix issues in all previous implementations, introducing DiffGrad -the first reliable module for exact backpropagation through DBP (see Fig.1). In §4, we show that even under the one-sample evaluation protocol, AutoAttack [10] significantly outperforms prior works, exposing their gradient fallacies. We further use a multi-sample evaluation that captures DBP 's stochasticity and resubmission risk-aligned with DiffHammer [41], which also identified the evaluation gap, but retained problematic gradients. By fixing both, we prove DBP even more vulnerable than they report, with robustness dropping below 17 . 19% . Finally, we show prior attack enhancements tailored to DBP (e.g., DiffHammer , DiffAttack [20]), being oblivious to the ability of standard gradient-based attacks to reshape its behavior, in fact, disrupt optimization, lowering attack performance, and confirming our theoretical scrutiny.

To replace the current inherently vulnerable single-evaluation DBP defense scheme, we propose a more robust majority-vote ( MV ) setup, where multiple purified copies are classified and the final decision is based on the majority label. Yet, even under MV , DBP retains only partial robustness against norm-bounded attacks-see §4.2, supporting our theoretical findings. As we established the inefficacy of intermediate projections, this resistance is due to DBP 's vast stochasticity: common AE s that introduce large changes to individual pixels are diluted and may not impact most paths. Instead, we require stealthy modifications that affect many pixels. In §5, we propose a novel adaptation of a recent strategy [21] from image watermarking that crafts low-frequency perturbations, accounting for links between neighboring pixels. This technique defeats DBP even under MV

Contributions. (i) Analytically scrutinizing adaptive attacks on DBP , proving they nullify its theoretical robustness claims. (ii) Addressing protocol and gradient issues in prior attacks, enabling reliable evaluations, and demonstrating degraded performance of DBP and the ineffectiveness of recent attack enhancement strategies [20, 41]. (iii) Introducing and evaluating a statistically grounded MV defense protocol for DBP . (iv) Proposing and adapting low-frequency ( LF ) attack optimizations to DBP , achieving unprecedented success even under MV . (v) Availability: aside from scalability and backpropagation issues, existing DBP implementations and attacks lack generalizability. We provide DiffBreak 1 -the first toolkit for evaluating any classifier with DBP under various optimization methods, including our novel LF , using our reliable DiffGrad module for backpropagation. (vi) Extensive evaluations on ImageNet and CIFAR-10 prove our methods defeat DBP , bringing its robustness to ' 0% , outperforming previous works by a large margin.

2 Background & Related Work

Adversarial Attacks. Given x P R d with true label y , classifier M , and preprocessing defense G ( G ' Id if no defense), attackers aim to generate a similar x adv s.t. M p G p x adv qq‰ y . Formally:

for loss ℓ M G . Typically, ℓ M G p x , y q ' ℓ p M p G p x qq , y q , where ℓ is a loss over M 's output that captures the desired outcome. For instance, ℓ p M p G p x qq , y q can be chosen as the probability that the classifier's output label is y , which we strive to minimize. D is a distance metric that ensures similarity if kept below some ϵ D . These untargeted attacks are the focus of many works [30, 40, 32, 29]. The expected value accounts for potential stochasticity in G (e.g., DBP below).

Diffusion models (DMs) [34, 36] learn to model a distribution p on R d by reversing the process that diffuses inputs into noise. DM s involve two stochastic processes. The forward pass converts samples into pure Gaussians, and is governed by the following SDE for an infinitesimal step dt ą 0 :

eq. (1) describes a stochastic integral whose solution up to t ˚ Pr 0 , 1 s gives x p t ˚ q . Here, f : R d ˆ R ÝÑ R d is the drift, w : R ÝÑ R d is a Wiener process, and g : R ÝÑ R is the diffusion coefficient. We focus on VP-SDE , which is the most common DM for DBP [30, 48, 40]. Yet, our insights generalize to all DM s (see [36] for a review). In VP-SDE , f p x , t q ' ´ 1 2 β p t q x p t q and g p t q ' a β p t q , where β p t q is a noise scheduler outputting small positive constants. These choices yield the solution:

for ϵ ' N p 0 , I d q and α p t q' e ´ ş t 0 β p s q ds . With proper parameters, we have x p 1 q' N p 0 , I d q . Thus, a process that inverts eq. (1) from t ˚ ' 1 to 0 allows generating samples in p from random noise. Due to Anderson [1], the reverse pass is known to be a stochastic process with:

Defining ˆ x p t ˚ q : ' x p t ˚ q , the process evolves from t ˚ to 0 with a negative time step dt and reverse-time Wiener process ¯ w p t q . Let p p x q be the probability of x under p , and p 0 t p ˜ x | x q the conditional density at t given x p 0 q ' x . Then, the marginal density is given by p t p ˜ x q ' ş p p x q p 0 t p ˜ x | x q d x , where p 0 ' p . Solving eq. (3) requires the score ∇ ˆ x p t q log p t p ˆ x p t qq , which can be approximated via a trained model s θ s.t. s θ p ˆ x p t q , t q « ∇ ˆ x p t q log p t p ˆ x p t qq [36], yielding:

As no closed-form solution exists, the process runs iteratively over discrete negative steps dt . Starting from t ˚ , d ˆ x is calculated at each i '| t dt | , until t ' 0 . This continuous-time DM describes a stochastic integral (despite the discretized implementations). An alternative, Denoising diffusion probabilistic modeling ( DDPM ) [19, 34], considers a discrete-time DM . The two are equivalent (see Appendix B).

DBP [30, 48, 40, 51] performs purification by diffusing each input x until optimal time t ˚ that preserves class semantics while still diminishing malicious interruptions. x p t ˚ q is then given to the reverse pass, reconstructing a clean ˆ x p 0 q« x s.t. ˆ x p 0 q' p for correct classification.

Certified vs. Empirical Robustness. While recent work has explored certified guarantees for DBP via randomized smoothing (RS) [48, 5, 55, 6, 45], these guarantees hold only under restrictive assumptions - e.g., small ℓ 2 perturbations and thousands of Monte Carlo samples per input. In contrast, empirical defenses [40, 30, 31, 7, 53] aim for practical robustness under realistic threats [10] and efficient inference. Like prior work [41, 20, 30, 40, 24], we explicitly target these empirical defenses-not orthogonal certified variants whose guarantees do not hold under stronger practical perturbations or operational constraints. Certification protocols are computationally prohibitive, and their bounds fail to capture threats that remain imperceptible but exceed certified radii.

3 Revisiting Diffusion-Based Purification

Westudy gradient-based attacks. In §3.1, we theoretically prove that adaptive attacks invalidate DBP 's principles. Then, we reconcile this with previous findings of DBP 's robustness, attributing them to

backpropagation issues and improper evaluation protocols. In §3.2, we analyze backpropagation mismatches in previous works and propose fixes. Finally, we present an improved evaluation protocol for DBP in §3.3 to better measure its robustness.

3.1 Why DBP Fails: Theoretical Vulnerability to Adaptive Attacks

DBP 's robustness is primarily attributed to its ability to project the purified ˆ x p 0 q onto the natural manifold [30, 48, 20]. This foundational assumption-rooted in the inherent behavior of the purification process-has remained unchallenged. In fact, the most advanced attacks have been explicitly tailored to exploit or circumvent it: DiffAttack [20] introduces suboptimal per-step losses to perturb the purification trajectory (see §4), while DiffHammer [41] constrains its optimization to feasible paths that evade detection by the DBP process itself. DBP is often justified through its marginal consistency: since s θ « ∇ log p t , t x p t qu t Pr 0 , 1 s and t ˆ x p t qu t Pr 0 , 1 s follow the same marginals [1], yielding ˆ x p 0 q ' p . Specifically, Xiao et al. [48] show that:

where p is the density of the natural data distribution and α p t ˚ q is the variance schedule at time t ˚ . Thus, DBP is expected to reject adversarial examples by construction: the probability of producing any ˆ x p 0 q that is both adversarial and lies off-manifold is exponentially suppressed by the score model. However, this reasoning assumes the reverse process remains faithful to p . In practice, the score function s θ is itself an ML model-differentiable and susceptible to adversarial manipulation. Our key insight is that traditional gradient-based attacks, when backpropagated through DBP , do not simply bypass the purifier-they implicitly target it, steering the score model to generate samples from an adversarial distribution. This challenges the assumptions underlying prior attack strategies, many of which distort gradients or constrain optimization in ways that ignore the score model's vulnerability, undermining their own effectiveness. Below, we formally characterize this vulnerability.

Definitions. Diffusion Process & Score Model. For t 1 ě t 2 , let ˆ x t 1 : t 2 represent the joint reverse diffusion trajectory ˆ x p t 1 q , ˆ x p t 1 ` dt q , . . . , ˆ x p t 2 q . Let s θ denote the score model used by DBP to approximate the gradients of the natural data distribution at different time steps. s θ t is the abstract score model invoked at time step t with parameters θ t , corresponding to s θ p¨ , t q . Given that the score model s θ is an ML model that interacts with adversarial input x , we denote the parameters at each reverse step as θ t x , capturing their dependence on x . That is, θ t x ' θ t p x q , which makes explicit that the purification process is not immutable , as adversarial modifications to x can shape its behavior.

Classifier. For a classifier M and label y , let M y p u q denote the probability that u belongs to class y .

Adaptive Attack. A gradient-based algorithm that iteratively updates x with learning rate η ą 0 :

Here, r ∇ x is the empirical gradient estimate over N purified samples ˆ x p 0 q n , obtained via Monte Carlo approximation and backpropagated through DBP 's stochastic process.

Theorem 3.1. The adaptive attack optimizes the entire reverse diffusion process , modifying the parameters t θ t x u t ď t ˚ such that the output distribution ˆ x p 0 q ' DBP t θ t x u p x q , where DBP t θ t x u p x q is the DBP pipeline with the score model's weights t θ t x u t ď t ˚ adversarially aligned. That is, the adversary implicitly controls the purification path and optimizes the weights t θ t x u t ď t ˚ to maximize:

Since t θ t x u t ď t ˚ depend on the purification trajectory ˆ x t ˚ :0 , optimizing x under the adaptive attack directly shapes the purification process itself , forcing DBP to generate adversarially structured samples that maximize misclassification.

Impact. As DBP is widely perceived as immutable, its robustness is often attributed to gradient masking (vanishing or explosion) due to its presumed ability to project inputs onto the natural manifold. However, this reasoning treats DBP as a static pre-processing step rather than a dynamic optimization target . Our result overturns this assumption : rather than resisting adversarial influence, DBP itself becomes an active participant in adversarial generation . Crucially, standard

adaptive attacks that backpropagate accurate gradients through DBP do not merely evade it-they implicitly exploit and reshape its behavior, forcing the purification process to align with the attacker's objective. The introduced perturbations directly shape the purification trajectory , causing DBP to generate, rather than suppress, adversarial samples. Thus, DBP does not inherently neutralize adversarial perturbations but instead shifts the optimization target from the classifier to the score model s θ , leaving this paradigm highly vulnerable.

Proof. (Sketch) The adaptive attack maximizes the probability that the classifier mislabels the purified output, which is expressed as an expectation over the stochastic purification process. Applying the law of the unconscious statistician (LOTUS), we reformulate this expectation over the joint distribution of the reverse diffusion trajectory, shifting the dependency away from the classifier's decision at the final step. Leveraging smoothness, we interchange differentiation and expectation, revealing that the adaptive attack's gradient corresponds to the expected gradient of the purification trajectory, which is governed by the score model's parameters. Crucially, these parameters are optimized implicitly through perturbations to x , rather than being explicitly modified. This demonstrates that the adaptive attack does not merely navigate DBP -it fundamentally shapes its behavior, exploiting the score model rather than directly targeting the classifier. The full proof is in Appendix C.

3.2 Precise DBP Gradients with DiffGrad

Building on our theoretical analysis, we examine why prior adaptive attacks [30, 40, 20, 26, 24] underperform and show how DiffGrad , provided by our DiffBreak toolkit, resolves these limitations.

We reserve the terms forward/reverse pass for DBP and forward/backpropagation for gradient computations. Let ˆ x p t ˚ q : ' x p t ˚ q . The reverse process follows:

and by chain rule the gradient of any function F of ˆ x p t ` dt q w.r.t. ˆ x p t q is:

Applying this recursively yields gradients w.r.t. ˆ x p t ˚ q , and via eq. (2), the input x . Yet, standard automatic differentiation is impractical for DBP due to excessive memory overhead from dependencies between all ˆ x p t q . Prior work resorts to approximations such as the adjoint method [25], or checkpointing [8] to compute the exact gradients. However, approximations yield suboptimal attack performance [24]. On the other hand, we identify critical issues in existing checkpointing-based implementations that previously led to inflated estimates of DBP 's robustness (see Appendix D for detailed analysis, DiffGrad 's pseudo-code, and empirical evaluations of backpropagation issues):

1) High-Variance Gradients: Gradient-based attacks require estimating expected gradients using N Monte Carlo (EOT) samples. When N is small, gradient variance is high, leading to unreliable updates. Prior works used small N due to limitations in how EOT samples were purified-one at a time via serial loops in standard attack benchmarks (e.g., AutoAttack [10]). DiffGrad parallelizes EOT purifications. This integrates seamlessly with standard attacks. Coupled with our termination upon success protocols-see §4.2, this enables us to use up to 128 EOT samples (for CIFAR-10 ) with a speedup of up to 41 ˆ upon early termination, drastically reducing variance.

2) Time Consistency: torchsde 2 is the de facto standard library for SDE solvers. Hence, several prior checkpointing approaches likely use torchsde as their backend. Yet, torchsde internally converts the integration interval into a PyTorch tensor, which causes a discrepancy in the time steps on which the score model is invoked during both propagation phases due to rounding issues if the checkpointing module is oblivious to this detail. DiffGrad ensures time steps match in both phases.

3) Reproducing Stochasticity: Forward and backward propagation should reuse identical randomness to preserve fidelity. In vanilla DBP , diffusion noise cancels in the gradient, so not preserving stochastic components has little effect. Yet, for guided schemes whose computations depend on randomness (some current ones and potential future variants), failing to reproduce the noise realizations can bias gradients and derail optimization. We thus introduce a structured Noise Sampler NS that records all noise during the forward pass and reuses it in backpropagation. We also enable deterministic CuDNN kernel selection to avoid backend nondeterminism-see Appendix D.1.3 for details.

4) Guidance Gradients: Guided DBP [40] uses guidance metrics along the reverse pass. This guidance is obtained by applying a guidance function g fn to (potentially) both the original input x and the reverse-diffused ˆ x p t q . As such, it creates paths from x to the loss that basic checkpointing fails to consider. Furthermore, the guidance itself is often in the form of a gradient, necessitating second-order differentiation during backpropagation, which is, by default, disabled by differentiation engines. We extend DiffGrad to include these 'guidance' gradients. Critically, recent SOTA DBP defenses generate purified outputs from pure noise, relying on x only via guidance (see §6). As such, the lack of support for guidance gradients in all previous implementations leads to a false sense of security. To our knowledge, DiffGrad is the first to account for this component.

5) Proper Use of The Surrogate Method [24]: Upon inspecting DiffHammer 's code, we find their checkpointing implementation effectively applies Lee and Kim [24]'s surrogate approximation to calculate the gradients, which slightly degrades gradient quality with no practical performance gains-see Appendix F. Yet, the real issue lies in DiffHammer 's implementation of the surrogate , which diverges from [24], further corrupting the gradients. We defer details to Appendix D.1.5.

3.3 On The Issues in DBP 's Evaluation Protocols.

DBP is typically deployed in a single-purification ( SP ) setting: an input x is purified once via a stochastic reverse process and classified as c ' M p ˆ x p 0 qq [30, 40]. This assumes ˆ x p 0 q lies on the natural manifold, yielding a correct label with high probability-see §3.1. Yet, prior studies [20, 30, 40] fail to assess this very property: they evaluate robustness by purifying only the final adversarial iterate, testing just a single stochastic path, yielding noisy, unrepresentative estimates.

DiffHammer [41] addressed this with worst-case robustness (Wor.Rob): the attack succeeds if any of N purifications (evaluated at each attack step) leads to misclassification. The metric is Wor.Rob : ' 1 ´ 1 S ř S j ' 1 max i Pr r N s s A p j q i , where A p j q i ' 1 if the i -th purification of sample j fails, and

S is the dataset size. They justify this protocol by modeling resubmission attacks (e.g., in login attempts), thereby limiting N to (typically) N ' 10 after which the attacker will be blocked. However, attackers can retry inputs arbitrarily in stateless settings like spam, CSAM, and phishing. Even in stateful systems, the defender has no control over the stochastic path. Thus, SP evaluations require many purifications per input for statistically meaningful conclusions.

Yet, any stochastic defense fails given enough queries [27]. Even if DBP nearly always projects to the manifold, SP is only reliable if misclassification probability is negligible over all paths-rare in practice (§4). Robust predictions must hence aggregate over multiple purifications. We thus propose:

Majority Vote (MV). Given input x , generate K purifications and predict by majority: c ' MV K p x q : ' mode t M p ˆ x p 1 q p 0 qq , . . . , M p ˆ x p K q p 0 qqu . Unlike certified smoothing [48], MV requires no excessive sampling, yet offers a stable, variance-tolerant robustness estimate, albeit without formal guarantees. We use the majority-robustness metric: MV.Rob : ' 1 ´ 1 S ř S j ' 1 ' MV K p x j q ‰ y j ‰ ,

ř

ř

✶ where y j is the ground-truth label. DiffHammer 's additional Avg.Rob : ' 1 ´ 1 NS S j ' 1 N i ' 1 A p j q i averages path-level failures across all samples, conflating individual copy failures with sample robustness. A few fragile samples can dominate this metric, making it unreliable for deployment.

4 Experiments

We reevaluate DBP , demonstrating its degraded performance when evaluation and backpropagation issues are addressed, cementing our theoretical findings from §3.1.

Setup. We evaluate on CIFAR-10 [22] and ImageNet [11] similar to previous work [41, 20, 30, 40]. We consider two foundational DBP defenses: The VP-SDE DBP ( DiffPure ) [30] and the Guided -DDPM (see §3.2), GDMP [40]. We use the DM s [12, 19, 36] studied in the original works, adopting the same purification settings-See Appendix E. Following Nie et al. [30], we use WideResNet-28-10 and WideResNet-70-16 [52] for CIFAR-10 , and WideResNet-50-2 and DeiT-S [14] for ImageNet . As in previous work [40, 30, 20, 41, 26, 24], we focus on the white-box setting and use AutoAttack -ℓ 8 ( AA -ℓ 8 ) [10] with ϵ 8 ' 8 { 255 for CIFAR-10 and ϵ 8 ' 4 { 255 for ImageNet . Existing works focus on norm-bounded ( ℓ 8 and ℓ 2 ). For DBP , ℓ 8 has repeatedly proven superior [20, 24, 26], making it the focus of our evaluations. We report clean accuracy ( Cl-Acc )-without attacks- and robust accuracy

( Rob-Acc )-the fraction of correctly classified attack samples. We use 256 random test samples per dataset, consistent with prior DBP work [41, 7]. Because DBP is a compute-intensive defense, we prioritize breadth over scale -two datasets ( CIFAR-10 , ImageNet ), multiple classifiers and DBP schemes, diverse attacks and baselines, and MV ablations-so readers see the same qualitative conclusions across settings (see §4- §6; extended results in Appendix F-Appendix H).

4.1 Reassessing One-Shot DBP Robustness with Accurate Gradients

As noted in §3, DBP 's robustness stems from two factors: inaccurate gradients and improper evaluation. As our work offers enhancements on both fronts, we evaluate each factor separately. Here, we isolate the gradient issue by re-running prior experiments under the same (problematic) single-evaluation protocol, but with accurate gradients via our DiffGrad module and compare the results to those from the literature. Despite using only 10 optimization steps (vs. up to 100 in prior work), our method significantly outperforms all gradient approximations and even recent full-gradient methods. For DiffPure , we lower robust accuracy from 62 . 11% (reported by Liu et al. [26]) to 48 . 05% , and for GDMP , from 24 . 53% (Surrogate [24]) to 19 . 53% . These results expose the issues in existing gradient implementations and invalidate claimed gains from enhancement strategies like DiffAttack . Full breakdowns and additional baselines are provided in Appendix F.

Evaluations Under Liu et al. [26]'s Protocol. Liu et al. [26], like DiffHammer [41] and our own analysis, note that evaluating a single purification at attack termination inflates robustness scores. To address this, they propose a refined 1-evaluation protocol, which tests 20 purifications of the final AE and declares success if any fail. This offers a stricter assessment than earlier one-shot methods, though still weaker than Wor.Rob (see §3.3). Accordingly, Liu et al. [26] group their method with one-shot evaluations. Repeating their setup using DiffGrad (20 attack iterations, N ' 10 EOT), we observe a dramatic drop in robust accuracy: on WideResNet-28-10, we improve upon Liu et al. [26]'s results by 25 . 39% and 30 . 42% for DiffPure and GDMP , respectively-bringing the Rob-Accs down to 30 . 86% and 10 . 55% . These results confirm the superiority of DiffGrad 's gradients and expose DBP 's realistic vulnerability. Detailed results are in Appendix G.

4.2 DBP Under Realistic Protocols

Here, we continue to highlight the shortcomings of one-shot evaluation and the strength of DiffGrad , while exposing the invalidity of previous attack enhancements over the standard gradient-based methodologies. To do so, we adopt a Wor.Rob protocol, similar to DiffHammer -see §3.3 and also include our majority-vote variant (MV.Rob). We reimplement DiffHammer and DiffAttack using DiffGrad , and compare them to their original versions from [41] and our standard AA -ℓ 8 . All evaluations use CIFAR-10 with WideResNet-70-16; We also report ImageNet results be-

Table 1: AA -ℓ 8 performance comparison on CIFAR-10 ( ϵ 8 ' 8 { 255 ) under realistic threat models. Metrics include Wor.Rob and MV.Rob under a 10-evaluation protocol. : indicates strategy is PGD .

low. Full denotes the standard AA attack that uses the full exact gradients (i.e., via checkpointing).

Choice of batch size ( N ): We set N ' 10 for CIFAR-10 to match [41] (which uses N ' 10 for both EOT and evaluation copies) and to balance robustness/gradient accuracy with runtime and memory; these values reflect practical deployment and evaluation constraints. For ImageNet , we choose N ' 8 for similar reasons. Ablations with larger N , latency measurements, and practical recommendations appear in Appendix H; complexity details are in Appendix D.1.3 and Appendix D.3.

Results. Table 1 reports Wor.Rob and MV.Rob scores. The attacks run for 100 iterations, terminating upon success. For all attacksFull , DiffAttack , and DiffHammer -DiffGrad yields significantly lower Wor.Rob compared to [41], confirming the gradient mismatches discussed in §3.2 (MV.Rob is unique to our work). This establishes the need for our reliable DiffGrad as an essential tool for

future progress in the field, given the repeated problems that continue to surface in implementations of the checkpointing method. With correct gradients (i.e., DiffGrad ), all three attacks yield Wor.Rob ă 20% ; for GDMP , ă 10% , exposing the failure of the single-purification defense and reinforcing the claim that a statistically resistant alternative (e.g., our MV .Rob) must be used with DBP . Similarly, this highlights the issues in the attack evaluation protocols that consider a single sample (i.e., 1-evaluation) as they drastically inflate robustness estimates.

Notably, minor Wor.Rob differences among attacks in this range where predictions are highly noisy reflect random variation, not real gains. Hence, we must focus on the MV.Rob when comparing the three: For the same N, our MV is strictly harder as it takes the majority label meaning success requires misclassifying ą t N { 2 u of the N purified copies, whereas Wor.Rob counts a single error. Thus, MV.Rob is an upper bound on Wor.Rob, which aligns with the empirical findings attained with DiffGrad , showing significant robustness gains. Violations arise only when our MV.Rob results are compared to the Wor.Rob values reported by DiffHammer [41] and reflect implementation differences in gradient computation. As DiffGrad removes backpropagation mismatches that can reduce gradient fidelity and inflate robustness (both Wor.Rob and MV.Rob), MV -versus-worst-case comparisons should be made using a common, DiffGrad implementation of each attack.

Throughout §4, we have thus far shown that DBP 's reported robustness has been overstated due to gradient inaccuracies. Yet, some recent works introduce DBP -specific attack augmentations to improve success rates, but these overlook our theoretical finding that accurate gradients alone can reshape DBP 's output distribution-rendering such enhancements unnecessary. DiffHammer builds on the assumption that DBP 's trajectories split into 'vulnerable' and 'non-vulnerable' groups, with misleading gradients from the latter, but our analysis (see Theorem 3.1 ) shows that correct differentiation allows the attack to steer DBP 's stochastic process toward adversarial outcomes, contradicting that fixed partition. Likewise, DiffAttack 's per-step losses artificially strive to alter the output distribution, ignoring the standard gradient-based attack's inherent ability to do so, which could lead to suboptimal optimization updates. Below, we show that both these methods offer no advantages over the standard (full-gradient) attack and can, in fact, be counter-productive.

Under MV.Rob, DiffAttack-DiffGrad and Full-DiffGrad are identical on DiffPure , and DiffHammer-DiffGrad leads to MV.Rob lower by a mere 1 . 17% , which amounts to only 3 samples out of 256 and is thus statistically insignificant. On GDMP , DiffHammer-DiffGrad performs significantly worse than both others. Hence, DiffHammer worsens attack performance in accordance with our theory. DiffAttack-DiffGrad matches Full-DiffGrad on DiffPure ; on GDMP , it shows a 2 . 35% edge, which despite the questionable statistical significance given the test set size, could indicate a potential advantage. Yet, our ImageNet comparisons below refute this hypothesis.

ImageNet. We evaluate AA -ℓ 8 on ImageNet using WideResNet-50-2 and DeiT-S classifiers under ϵ 8 ' 4 { 255 ( 100 iterations), following standard practice. For DeiT-S, we also reim-

plement DiffAttack via DiffGrad for comparison. We use 16 EOT samples (two batches of N ' 8 ) and 8 samples for prediction (Wor.Rob/MV.Rob). As with CIFAR-10 , robustness drops sharply: Wor.Rob ranges from just 12 . 11% to 21 . 09% , while MV.Rob peaks at 32 . 83% . This confirms the vulnerability of single-purification and the strength of gradient-based attacks. DiffAttack underperforms our standard attack by 9 . 4% MV.Rob on DeiT-S, reinforcing its inferiority.

5 Defeating Increased Stochasticity

DBP 's stochasticity boosts its robustness under MV (see §4.2). Typical adversarial strategies incur high-frequency changes as they directly operate on pixels, altering each significantly w.r.t. its neighbors. This leads to visual inconsistencies, limiting the distortion budget. Such modifications are also easily masked by DBP 's noise. Instead, systemic, low-frequency ( LF ) changes allow larger perturbations and resist randomness.

Our LF method is inspired by a recent attackUnMarker [21]-on image watermarking that employs novel units termed Optimizable Filters (OFs) . In signal processing, a filter is a smoothing operation

defined by a kernel K P R M ˆ N ` (with values that sum to 1 ), with which the input is convolved. The output at each pixel is a weighted average of all pixels in its M ˆ N vicinity, depending on the weights assigned by K . Hence, filters incur systemic changes. Yet, they apply the same operation universally, unable to produce stealthy AE s, as the changes required to alter the label will be uniformly destructive. OFs allow each pixel p i, j q to have its own kernel K i,j to customize the filtering at each point. K ˚ is the set of all per-pixel K i,j s. The weights θ K ˚ are learned via feedback from a perceptual metric ( lpips ) [56], leading to an assignment that ensures similarity while maximizing the destruction at visually non-critical regions to optimize a specific objective. Note that the lpips constraint replaces the traditional norm constraint. To guarantee similarity, they also impose geometric constraints via color kernels σ c , similar to guided filters (details in Appendix I.1).

We subject x to a chain B ś OF ' OF K ˚ 1 , x ,σ c 1 ˝ ¨ ¨ ¨ ˝ OF K ˚ B , x ,σ c B of OFs similar to UnMarker , replacing the objective pertaining to watermark removal in the filters' weights' learning process with the loss over M . Each OF has a kernel set K ˚ b (with wights θ K ˚ and shape M b ˆ N b ), and σ c . We optimize:

ℓ M G denotes any loss as defined in §2. δ is a modifier that directly optimizes x , similar to traditional attacks. AE s are generated by manipulating x via δ and propagating the result through the filters. While direct modifications alone do not cause systemic changes, with OF s, they are smoothed over neighbors of the receiving pixels. δ allows disruptions beyond interpolations. Similar to UnMarker , we chain several OFs with different shapes to explore various interpolations. Optimization is iterative (code in Appendix I.3). max t lpips p x , B ś OF ( x ` δ qq ´ τ p , 0 u enforces similarity: If the distance exceeds τ p , the lpips gradients lower it in the next iteration. Otherwise, it returns 0 , minimizing ℓ M G unconditionally. This gives a solution within the τ p constraint (violating outputs are discarded), yielding optimal t p θ K ˚ b u , p δ s.t. x adv ' B ś z OF p x ` p δ q , where B ś z OF are the filters with t p θ K ˚ b u .

5.1 DBP Against Low-Frequency AE s

Our final question is: Can DBP be degraded further under MV ? Based on §5, this is possible with LF , which we test in this section. For LF (see §5), we use VGG-LPIPS [56] as the distance metric with τ p ' 0 . 05 , ensuring imperceptibility [17, 21]. Remaining parameters are similar to UnMarker 's (see Appendix I.2). We use 128 EOT samples for CIFAR-10 (same for label predictions since increasing the

sample set size leads to enhanced robustness of DBP -see Appendix H). For ImageNet , the numbers are identical to §4.2 (note that the dimensionality of ImageNet makes larger sample sets prohibitive and our selected set sizes reflect realistic deployments-the largest number of samples that can fit into a modern GPU simultaneously).

Choice of Perceptual Constraint : We use lpips with LF because it is widely adopted, and prior work [21, 17] provides known thresholds we can reuse for adversarial optimization. For AE s, calibrated thresholds are essential; otherwise, an overly permissive constraint can label visibly altered adversarial images as successful, which defeats the point and inflates attack success (i.e., underestimates robustness). Both independently calibrating other non-norm-bounded metrics (e.g., via user studies) and re-running robustness evaluations are time-consuming and require additional resources. Thus, we limit our scope to lpips but encourage future work to reproduce our experiments with alternative perceptual metrics for which calibrated thresholds may exist or become available.

Results. The LF results (using Full-DiffGrad for backpropagation) are in Table 3. We also include a ResNet-50 classifier for ImageNet . Not only does it defeat all classifiers completely, leaving the strongest with Rob-Acc of 3 . 13% , but it also does so in the MV setting, where previous attacks fail.

Concluding Remarks. Our findings highlight a limitation in current robustness evaluations, which focus heavily on norm-bounded attacks while overlooking powerful alternatives like low-frequency

( LF ) perturbations. Though not norm-bounded, LF is perceptually constrained-similar to StAdv [47], a longstanding benchmark against DBP Nie et al. [30]. LF 's imperceptibility is guaranteed due to using a perceptual threshold τ p ' 0 . 05 that has previously been proven to guarantee stealthiness and quality [17, 21]. We include qualitative results in Appendix J confirming this. One may question if existing attacks like StAdv can also defeat DBP under MV , rendering LF incremental. We address this in Appendix J, showing StAdv fails to produce stealthy AE s in this setting. While other techniques may also be adaptable to attacking certain DBP variants in the future, LF enjoys a solid theoretical foundation such alternatives may lack, limiting their generalizability to all DBP defenses.

Future Extensions. While we focus on vision models similar to earlier DBP work, both Theorem 3.1 and DiffGrad are modality-agnostic: they depend only on the diffusion dynamics and implementation, not structure. We thus expect the same vulnerabilities for, e.g., speech or video purification. The arguments in support of our LF attack's efficacy due to its low-frequency nature also hold across various domains. Yet, the specific implementation that relies on spectral filter networks would require domain-based adaptations to apply it to different tasks (e.g., replacing 2D Fourier filters with their 1D counterparts for audio). We therefore urge future work to extend our methods to other modalities.

6 Potential Countermeasures

Adversarial Training (AT). While AT remains a leading defense, it performs poorly on unseen threats. As expected, it fails against our LF . On an adversarially trained WideResNet-28-10 for CIFAR-10 ( DiffPure ), LF reduces robust accuracy to just 0 . 78% , confirming this limitation.

SOTA DBP : MimicDiffusion . One might ask whether recent variants offer improved robustness. Most build incrementally on the foundational defenses in §4, meaning our results broadly generalize. One notable exception is MimicDiffusion [35], which generates outputs entirely from noise, using the input only as guidance (see §3.2). Its goal is to preserve semantic content for classification while eliminating adversarial perturbations, and it reports SOTA robustness to adaptive attacks.

However, based on our theoretical analysis, we hypothesize this robustness is illusory-an artifact of improper evaluation and broken gradient flow. Unlike GDMP , which involves both direct and guidance paths from x to the loss, MimicDiffusion relies solely on guidance. Since guidance gradients require second-order derivatives (disabled by default), the original paper fails to compute meaningful gradients, severely overestimating robustness. We correct this using DiffGrad , the first method to properly differentiate through guidance paths. On CIFAR-10 , using AA -ℓ 8 (we exclude LF for time limitations) with N ' 128 for both EOT and evaluation, we find that the original Rob-Acc scores of 92 . 67% (WRN-28-10) and 92 . 26% (WRN-70-16) collapse under proper evaluation: Wor.Rob drops to 2 . 73% and 4 . 3% , respectively. Even under stricter MV.Rob, MimicDiffusion performs worse than the standard DBP defenses from §4, with accuracies of just 25 . 78% and 27 . 73% . This confirms that MimicDiffusion 's robustness is not real, and collapses under proper gradients.

Outlook. Our findings highlight the need for more robust defenses. DBP remains promising as it improves clean accuracy compared to prior purification methods. Yet, Theorem 3.1 shows it is vulnerable to adaptive attacks when accurate gradients are available . We believe future work should explore DBP variants that relax the assumptions of Theorem 3.1 . One possible direction is to modify the purification process at inference so that the model follows private stochastic dynamics that are not directly exposed to adversaries. Such approaches, if carefully designed to avoid gradient masking [2], could reduce the transferability of attacker-optimized gradients and increase robustness.

7 Conclusion

We scrutinized DBP 's theoretical foundations, overturning its core assumptions. Our analysis of prior findings revealed their reliance on inaccurate gradients, which we corrected to enable reliable evaluations, exposing degraded performance under adaptive attacks. Finally, we evaluated DBP in a stricter setup, wherein we found its increased stochasticity leaves it partially immune to normbounded AE s. Yet, our novel low-frequency approach defeats this defense in both settings. We find current DBP is not a viable response to AE s, highlighting the need for improvements.

Acknowledgements. This work was supported by NSERC Discovery Grant RGPIN-2020-04722.

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A Broader Impact & Limitations

This work advances adversarial robustness by exposing a fundamental vulnerability in DiffusionBased Purification ( DBP ). We show that adaptive attacks do not merely circumvent DBP but repurpose it as an adversarial generator, invalidating its theoretical guarantees. While this insight highlights a critical security risk, it also provides a foundation for designing more resilient purification strategies. To facilitate rigorous and reproducible evaluation, we introduce DiffBreak , an open-source toolkit providing the first reliable gradient module for DBP -based defenses, in addition to a wide array of attack implementations, including our low-frequency ( LF ) strategy that outperforms existing approaches, seamlessly applicable to a broad range of classifiers. Similar to existing adversarial attack toolkits (e.g., Foolbox [33], AutoAttack [10]), our framework is intended for research and defensive purposes. While this tool enhances robustness assessments, we acknowledge its potential misuse in adversarial applications. To mitigate risks, we advocate its responsible use for research and defensive purposes only. Finally, we urge developers of ML security systems to integrate our findings to design more resilient defenses against adaptive attacks. We encourage future research to explore fundamentally secure purification methods that are inherently resistant to manipulations.

Limitations. Our work focuses on dissecting the robustness of DBP defenses, both theoretically and empirically, with an emphasis on attack strategy. While we briefly consider existing mitigation techniques, future work should explore how diffusion models can be more effectively leveraged for defense. Classifiers could also be adversarially trained on LF perturbations to improve robustness. Yet, the vast hyperparameter and architecture space of LF potentially creates an effectively infinite threat surface, limiting the practicality of adversarial training. We leave this to future investigation.

While we do not report formal error bars or confidence intervals, this decision aligns with standard practice in the literature (e.g., [20, 26]) due to the high computational cost of gradient-based DBP attacks. Instead, we perform extensive experiments and also provide repeated empirical trials and variance analyses in Appendix D.2 that confirm our conclusions are robust, despite the absence of formal statistical intervals.

Although our main text focuses on conceptual and empirical issues in DBP , Appendix D.1.3 and Appendix D.3 provide theoretical and asymptotic cost analysis, and Appendix H presents latency measurements and real-world speedup comparisons. Our module is efficient, scales linearly with diffusion steps, and outperforms prior implementations in both latency and throughput. Thus, while cost is not emphasized in the main paper, it is extensively addressed and poses no limitation in practice. Nonetheless, even with our efficient implementation, the dominant cost from DBP itself is inherited by attacks and robustness evaluations, rendering them costly regardless. That said, DBP 's practicality may improve with advanced hardware or more efficient schemes in the future.

B Equivalence of DDPM and VP-SDE

An alternative to the continuous-time view described in §2 (i.e., VP-SDE ) is Denoising diffusion probabilistic modeling ( DDPM ) [19, 34], which considers a discrete-time framework ( DM ) where the forward and reverse passes are characterized by a maximum number of steps T . Here, the forward pass is a Markov chain:

where z i ' N p 0 , I d q and β i is a small positive noise scheduling constant. Defining dt ' 1 T , we know due to Song et al. [36] that when T ÝÑ8 (i.e, dt ÝÑ 0 , which is the effective case of interest), this converges to the SDE in eq. (1) (with the drift and diffusion function f and g described in §2). The reverse pass is also a Markov chain given as:

When T ÝÑ8 , d ˆ x converges to eq. (4) (see [36]). Thus, the two views are effectively equivalent. Accordingly, we focus on the continuous view, which encompasses both frameworks. For discrete time, x p t q will be used to denote x | t dt | .

C Proof of Theorem 3.1

Theorem 3.1. The adaptive attack optimizes the entire reverse diffusion process , modifying the parameters t θ t x u t ď t ˚ such that the output distribution ˆ x p 0 q ' DBP t θ t x u p x q , where DBP t θ t x u p x q is the DBP pipeline with the score model's weights t θ t x u t ď t ˚ adversarially aligned. That is, the adversary implicitly controls the purification path and optimizes the weights t θ t x u t ď t ˚ to maximize:

Proof. The adversary aims to maximize:

Expanding this expectation yields the following alternative representations:

The first transition is due to the definition of expectation, the second follows from the definition of marginal probability, and the final transition replaces the joint density function with its compact form.

Since this formulation abstracts away x and t θ t x u t ď t ˚ , we explicitly include them as p p ˆ x t ˚ :0 q ' p p ˆ x t ˚ :0 | x , t θ t x u t ď t ˚ q . For notation simplicity, we define p θ x p ˆ x t ˚ :0 | x q ' p p ˆ x t ˚ :0 | x , t θ t x u t ď t ˚ q . Thus, the final optimization objective is:

Since we assume smoothness ( C 2 ), we interchange gradient and integral:

where the last step is because Pr p␣ y | ˆ x p 0 qq does not depend on x , but only on ˆ x p 0 q which is independent of x (though its probability of being the final output of DBP is a function of x ). Optimizing the objective via gradient ascent relies on altering DBP 's output distribution alone, evident in its gradient where Pr p␣ y | ˆ x p 0 qq assigned by the classifier is a constant with its gradient ignored. While we lack direct access to the gradients of the probabilistic paths above, we may still attempt to solve the optimization problem.

Recall that by definition, @ u M y p u q ' Pr p y | u q . Thus, the required gradient can also be expressed as:

Yet, this expectation is over probabilistic paths whose randomness is due to the noise ϵ of the forward pass and the Brownian motion d ¯ w t at each reverse step t that are independent. Hence, by the law of the unconscious statistician:

where p r p ϵ , d ¯ w t ˚ , ..d ¯ w 0 q denotes the joint distribution of the noise ϵ and the Brownian motion vectors in the reverse pass. Note that ˆ x p 0 q on the RHS denotes the output obtained by invoking the

DBP pipeline with some assignment of these random vectors on the sample x . As earlier, we can interchange the derivation and integration, obtaining:

Let G x denote the random variable that is assigned values from ∇ x M y p ˆ x p 0 qq , where ˆ x p 0 q is as described above, and denote its covariance matrix by Σ G x . Essentially, we are interested in E r G x s . If we define r ∇ x as:

where each ˆ x p 0 q n is the output of DBP invoked with a certain random path p ϵ n , d ¯ w n t ˚ , ..d ¯ w n 0 q i.i.d ' p p ϵ , d ¯ w t ˚ , ..d ¯ w 0 q and N is a sufficiently large number of samples. Then due to the central limit theorem, r ∇ x ÝÑ N p E r G x s , Σ Gx N q . That is, propagating multiple copies through DBP and then averaging the loss gradients computes the required gradient for forcing DBP to alter its output distribution. The larger the number N of samples is, the lower the variance of the error, as can be seen above. Note that the adaptive attack operates exactly in this manner, assuming it uses M y as the loss it minimizes (but the soundness of the approach generalizes intuitively to any other loss with the same objective over the classifier's logits), proving our claim.

D Details on Our DiffGrad Gradient Module

In Appendix D.1, we identify key implementation challenges in prior work, detailing how DiffGrad systematically resolves each one. Then, in Appendix D.2, we empirically demonstrate their impact on DBP 's gradients when left unaddressed, reinforcing their practical significance and validating the need for our reliable module. Appendix D.3 presents the pseudo-code for our memory-efficient checkpointing algorithms, offering a transparent blueprint for reproducible and correct gradientenabled purification. Finally, in Appendix D.4, we verify the correctness of our implementation, confirming that the gradients computed by DiffGrad match those produced by a true differentiable purification pipeline.

D.1 The Challenges of Applying Checkpointing to DBP and How DiffGrad Tackles Them

D.1.1 High-Variance Gradients

The challenge of high-variance gradients due to insufficient EOT samples is introduced in §3.2. We defer its empirical analysis to Appendix D.2, where we quantify the gradient variability under different sample counts. Practical implications for performance and throughput-enabled by DiffGrad 's design-are explored in the ablation study in Appendix H. Accordingly, we focus below on the remaining implementation issues.

D.1.2 Time Consistency

Rounding issues may emerge when implementing checkpointing over torchsde solvers: Given the starting time t ˚ , the solver internally converts it into a PyTorch tensor, iteratively calculating the intermediate outputs by adding negative time increments to this tensor. On the other hand, checkpointing requires re-calculating the intermediate steps' samples during back-propagation. If this code is oblivious to torchsde 's conversion of the initial time into a PyTorch tensor, it will continue to treat it as a floating point number, updating it with increments of the time step to obtain each intermediate t used to re-compute the dependencies. The PyTorch implementation does not aim for 100% accuracy, leading to minute discrepancies in the current value of t compared to pure floating-point operations. These inaccuracies accumulate over the time horizon, potentially severely affecting the gradients. Instead, we ensure both the solver and checkpointing code use the same objects (either floating points or tensors).

D.1.3 Reproducing Stochasticity

CuDNN-Induced Nondeterminism. We found that even in deterministic purification pipelines, subtle nondeterminism from PyTorch's backend can cause discrepancies between forward and backward propagations. Specifically, CuDNN may select different convolution kernels during the recomputation of intermediate states in checkpointing, leading to minute numerical drift.

To eliminate this, DiffBreak explicitly forces CuDNN to behave deterministically, guaranteeing consistent kernel selection and numerical fidelity. While this source of error is subtle, it is measurable: for DiffPure with t ˚ ' 0 . 1 and dt ' 0 . 001 , we observed raw and relative gradient discrepancies of 1 e ´ 4 and 7 . 28 e ´ 5 when all other issues have been addressed. With this fix, the discrepancy dropped to exactly zero. Although less severe than other sources of error (e.g., time inconsistency or missing gradient paths), this level of precision is critical in setups where gradients are small to prevent sign changes that can affect optimization trajectories. Our inspection of prior work's code reveals this drift was not previously addressed.

Noise Sampler for Guidance Robustness. While the contribution of the stochastic component of d ˆ x often cancels analytically in vanilla VP-SDE -style purification (see §2), meaning it does not affect the gradient and therefore is not required to be accurately reproduced during checkpointing, this is not guaranteed in all variants. In particular, many guidance-based schemes-see §3.2-integrate stochastic terms within the guidance function itself. That is, the guidance function may incorporate stochasticity. When this occurs, gradients become sensitive to noise realizations, and failure to preserve them could break correctness. Yet, standard checkpointing only stores the intermediate ˆ x p t q s. Hence, ˆ x p t ` dt q will differ between the propagation phases as d ˆ x is computed via different random variables.

We restructure the logic computing d ˆ x : We define a function calc _ dx that accepts the noise as an external parameter and utilize a Noise Sampler NS , initialized upon every forward propagation. For each t , NS returns all the necessary random noise vectors to pass to calc _ dx . Instead of ˆ x p 0 q only, forward propagation also outputs NS and a state S containing all ˆ x p t q s. These objects are used to restore the path in backpropagation. This design also future-proofs DiffBreak for emerging guided or hybrid purifiers: any randomness on which the guidance depends is captured by NS and replayed exactly during differentiation.

The memory cost of our design is O p t ˚ | dt | q , storing only NS , and all ˆ x p t q s, each with a negligible footprint ( O p 1 q ) compared to graph dependencies [20].

D.1.4 Guidance Gradients

In schemes that involve guidance, it is typically obtained by applying a function g fn to ˆ x p t q at each step (note that g fn may involve stochasticity-see Appendix D.1.3-as is often the case in GDMP [40]). For instance, in Guided -DDPM [40], the original sample x is used to influence the reverse procedure to retain key semantic information, allowing for an increased budget t ˚ to better counteract adversarial perturbations. Effectively, it modifies eq. (8) describing the reverse pass of DDPM as:

where GC is a guidance condition (typically a distance metric), each step minimizes by moving in the opposite direction of its gradient, while the scale s controls the guidance's influence.

That is, in the specific case of Guided -DDPM , g fn p ˆ x p t qq ' ´ ∇ ˆ x p t q GC p ˆ x p t q , x q , where GC is a distance metric. Nonetheless, other choices for g fn may be employed in general. Typically, as the goal of the guidance is to ensure key information from the original sample x is retained, g _ fn will also directly involve this x in addition to ˆ x p t q (e.g., GC above). Yet, a naive implementation would back-propagate the gradients to x by only considering the path through ˆ x p t q . Yet, when g _ fn relies on a guide constructed from x to influence ˆ x p t q (e.g., guide ' x in Guided -DDPM , it creates additional paths from x to the loss through this guide at each step t . Accordingly, DiffGrad augments the process to include the gradients due to these paths. In the general case, this guide may not be identical to x but can rather be computed based on x or even completely independent (in which case no guidance gradients are collected). DiffGrad captures this nuance through an abstract function g _ aux that, given x , outputs the guide . Similar to eq. (6) , we have that for each t , the

gradient of any function F applied to ˆ x p 0 q w.r.t. guide due to the path from ˆ x p t ` dt q to ˆ x p 0 q is given by:

as ˆ x p t ` dt q is a function of guide . Recall that we are interested in F , which is the loss function over the classifier's output on ˆ x p 0 q . The gradient of F w.r.t. guide is a superposition of all these paths' gradients, given as:

By the chain rule, F 's gradient w.r.t x due to the guidance paths, which we denote as ∇ g x F , is:

As a convention, for an unguided process or when guide and x are not related, we define the gradient returned from eq. (11) as ∇ g x F ' 0 , preserving correctness in general. Since x in this guided scenario traverses both the guidance and standard purification paths, the final gradient is the sum of both components.

Finally, automatic differentiation engines, by default, generate gradients without retaining dependencies on the inputs that produced them. Thus, when the guidance itself is in the form of a gradient as in the case of Guided -DDPM or other potential alternatives, its effects will not be back-propagated to x through any of the two paths described above, despite our proposed extensions. DiffGrad alters this behavior, retaining the dependencies of such gradient-based guidance metrics as well.

D.1.5 Proper Use of The Surrogate Method [24]

As noted in §3.2, DiffHammer [41] adopts the surrogate method (originally proposed by Lee and Kim [24]) for gradient computation, as acknowledged in their Appendix C.1.1. This approach approximates DBP 's gradients by replacing the standard fine-grained reverse process (e.g., dt ' 0 . 001 ) with a coarser one (e.g., s dt ' 0 . 01 ), thereby enabling memory-efficient differentiation using standard autodiff. For instance, when using a diffusion time t ˚ ' 0 . 1 for DBP (see §2), the finegrained process would require 100 steps, which is computationally infeasible (memory-exhaustive) for gradient computation without checkpointing. In contrast, the coarse-grained process would only require 10 steps, which is possible.

Specifically, the forward pass (diffusion) is computed using the closed-form solution from eq. (2), while the reverse pass uses s dt , enabling efficient gradient computation. Notably, this replacement only occurs for the purpose of updating the attack sample (i.e., computing the gradients) and happens during both forward and backpropagation so that the two phases match. In contrast, when evaluating the generated AE , it is purified via the standard fine-grained process that uses dt , as this is the true (full) procedure the model owner (defender) would execute. Although the surrogate process yields approximate gradients for a slightly different process, Lee and Kim [24] found it effective and more accurate than other approximations like the adjoint method [25] (despite remaining slightly suboptimal-see Appendix F).

However, a manual inspection of DiffHammer 's code 3 reveals that their implementation of this surrogate method contains a critical issue. Rather than computing the reverse process with the coarse s dt as intended for attack optimization during both forward and backpropagation, they first run the reverse pass during forward propagation with the standard dt , storing intermediate states. Then, during backpropagation, they attempt to backpropagate gradients using checkpoints spaced at s dt intervals, but instead reuse the stored dt -based forward states. This leads to a mismatch: gradients intended for steps of size s dt are applied to states computed with dt , effectively disconnecting the computation graph and introducing significant gradient errors. In practice, this behaves like a hybrid between checkpointing and BPDA [2], where gradients are approximated around fixed anchor points without correctly tracking the reverse dynamics.

As we show in §4.2, this implementation leads to significant attack performance degradation compared to the full gradients. It illustrates the fragility of gradient computation in diffusion attacks and further motivates the need for our reliable DiffGrad module.

D.2 Demonstrating The Effects of Incorrect Backpropagation

We empirically demonstrate the impact of the identified issues on DBP 's gradients in Fig. 2 and briefly explain each result below. As numerical results for CuDNN-induced nondeterminism (i.e., unhandled stochasticity) are already presented in Appendix D.1.3, we focus here on the remaining four issues detailed in Appendix D.1:

(a) Effect of insufficient EOT samples. Fig.2a illustrates the impact of using too few EOT samples when computing gradients-see§3.2 and Appendix D.1.1. While prior works [41, 20, 24, 26, 30] typically use 10-20 samples, such low counts, while somewhat effective, may introduce significant variance, resulting in noisy gradients and suboptimal attacks.

To quantify this, we run the following experiment on a CIFAR-10 sample x purified with DiffPure ( t ˚ ' 0 . 1 , dt ' 10 ´ 3 ). For each EOT count N (shown on the x-axis), we generate N purified copies, compute the average loss, and backpropagate to obtain the EOT gradient. This is repeated 20 times to yield 20 gradients g N 1 , . . . , g N 20 for each N . We then define:

This metric reflects the worst-case deviation between gradients under repeated EOT sampling. By the central limit theorem (see Appendix C), the variance of EOT gradients decays with N , and thus g mean d p N q Ñ 0 as N Ñ8 . The curve in Fig. 2a captures this decay and lets us identify a threshold where variance becomes acceptably low.

The plot confirms that gradient variance decreases sharply with the number of EOT samples. While N ' 10 -the typical choice in prior work-is somewhat effective and viable under resource constraints, it remains suboptimal. We observe that variance continues to drop until around N ' 64 , after which it plateaus. This suggests that although larger N values like 128 yield marginally better stability, the bulk of the benefit is realized by N ' 32 -64 . Thus, N ' 10 is a practical baseline, but N ě 64 should be preferred when accuracy is critical and compute allows, coroborating our claims in §3.2.

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(b) Effect of time inconsistency. As detailed in §3.2 and Appendix D.1.2, rounding inconsistencies can emerge when using checkpointing with torchsde solvers. These stem from how the solver internally handles time as a PyTorch tensor, which may diverge subtly from floating-point representations if not carefully synchronized. While such discrepancies are negligible for short purification paths (small t ˚ ), they accumulate significantly over longer trajectories-particularly at standard DBP settings like t ˚ ' 0 . 1 with dt ' 10 ´ 3 (i.e., 100 reverse steps), as in DiffPure on CIFAR-10 .

To quantify this effect, we purify a fixed CIFAR-10 sample x using values of t ˚ from 0 . 005 to 0 . 1 in steps of 0 . 005 . For each t ˚ , we compute gradients using DiffGrad under two conditions: (1) without correcting the inconsistency (yielding g nf ), and (2) with the issue fixed (yielding g f ), both using the same stochastic path. We then compute two metrics: (1) g d ' } g f ´ g nf } 2 (absolute error), and (2) g e ' } g f ´ g nf } 2 } g f } 2 (relative error). These quantify the divergence introduced by uncorrected rounding-both in magnitude and in proportion to the true gradient-and illustrate its increasing severity with longer reverse trajectories.

Fig. 2b confirms that even minute rounding discrepancies in time handling, if uncorrected, can completely corrupt gradients over longer diffusion trajectories. Both the absolute error g d (blue) and the relative error g e (orange) grow rapidly with t ˚ . By t ˚ ě 0 . 03 , g e exceeds 90% , and for the typical setting of t ˚ ' 0 . 1 , the relative error reaches 100% , indicating that the gradients are nearly orthogonal to the correct direction. This validates our claim that unpatched checkpointing introduces severe errors and demonstrates that our DiffGrad fix is essential for correct gradient computation in practical DBP setups.

(c) Effect of ignored guidance gradients. We evaluate the impact of neglecting guidance gradients, a critical problem in current attacks against Guided DBP defenses (e.g., GDMP , MimicDiffusion )-see §3.2 and Appendix D.1.4. As explained earlier, guidance introduces additional gradient paths from the input x to ˆ x p t q , typically requiring second-order derivatives to capture. Existing approaches ignore these paths, leading to incomplete gradients and suboptimal attacks. To our knowledge, DiffGrad is the first system to correctly handle them.

To quantify this effect, we purify a fixed CIFAR-10 sample x using GDMP (setup in Appendix E) while varying the purification horizon t ˚ P t 0 . 006 , 0 . 012 , . . . , 0 . 036 u . For each t ˚ , we compute gradients using DiffGrad with and without accounting for guidance-yielding g f and g nf , respectively-under the same stochastic path. We then compute the absolute and relative gradient error ( g d , g e ) as in previous experiments.

The findings in Fig. 2c clearly demonstrate the severe impact of neglecting guidance gradients in Guided DBP setups. Both the raw error ( g d ) and the relative error ( g e ) increase steeply with t ˚ , confirming that as the purification path grows longer, the omitted gradient paths-stemming from guidance dependencies-dominate the overall gradient signal. Most notably, g e exceeds 10 4 at t ˚ ' 0 . 036 , indicating that the gradient used in prior works is essentially meaningless for optimization, as it no longer aligns with the true direction of steepest descent.

These findings directly explain the poor attack success rates previously observed on guided defenses like GDMP and MimicDiffusion , and reinforce why our attacks, which correctly account for these guidance gradients via DiffGrad , achieve drastically superior performance-see §4.2 and §6. In short, the guidance mechanism, when improperly handled, not only fails to help but actively hinders attack effectiveness by yielding incorrect gradient signals.

(d) Effect of incorrect surrogate gradients. As explained in §3.2 and Appendix D.1.5, prior work [41] uses the surrogate method [24] to enable efficient gradient computation for DBP . However, we identify a critical divergence in DiffHammer 's [41] implementation of this method that substantially compromises attack performance. This not only leads to inflated robustness estimates for DBP , but also to misleading conclusions about the relative effectiveness of the standard gradientbased attacks versus DiffHammer 's proposed enhancements-see §4.2. Specifically, as detailed in Appendix D.1.5, DiffHammer mismatches the time discretization used in the forward and backward passes: the forward pass computes intermediate denoised states ˆ x p t q using a fine step size dt , while the backward pass attempts to propagate gradients at a coarser granularity s dt ą dt using those same (misaligned) forward states. This inconsistency leads to gradients being applied to states generated under a different dynamics, corrupting the computation and severely degrading the attack.

To validate this, we conduct a final experiment: For three different values of dt P t 0 . 001 , 0 . 005 , 0 . 01 u and fixed t ˚ ' 0 . 1 , we purify a fixed CIFAR-10 sample x . For each dt , we evaluate four surrogate variants using s dt P t dt, 2 dt, 5 dt, 10 dt u . For every configuration, we compute g nf using DiffHammer 's surrogate implementation and g f using the correct implementation. As before, we report both g d and g e to quantify the absolute and relative gradient error due to the mismatch between dt and s dt . Each experiment is repeated 10 times, and we report the mean values.

The results in Fig. 2d clearly validate our claim: the gradient errors induced by DiffHammer 's surrogate implementation grow substantially with increasing s dt { dt , saturating quickly even for modest mismatches. Both absolute error g d and relative error g e consistently worsen across all dt configurations, indicating that gradients are being applied to the wrong points in the computation graph.

Crucially, DiffHammer uses dt ' 0 . 01 and s dt ' 2 dt ' 0 . 02 , a setup which already produces substantial degradation ( g d « 3 , g e « 1 ), confirming that their reported results rely on gradients that diverge significantly from the correct ones. These errors propagate into the attack, weakening its effectiveness and misleadingly suggesting that first-order attacks are inherently inferior. This experiment conclusively demonstrates that DiffHammer 's surrogate misuse is not a minor detail, but a critical bug that undermines their central claims.

We note that DiffGrad also provides a correct implementation of the surrogate method (despite the full correct gradient being the main method considered in the paper).

D.3 Pseudo-Code for Our Memory-Efficient Gradient-Enabled Purification with DiffGrad

Algorithm 1 Differentiable Purification with DiffGrad -Forward Propagation

Forward Propagation. DiffGrad 's forward propagation logic is in Algorithm 1. The code in blue is optional, pertaining to the use of guidance. We highlight in red the portions that differ from standard forward propagation. First, we generate the guidance guide from x (line 1) and disable all graph dependency storage (line 2), enabling our code to run efficiently without attempting to store graphs that will lead to memory failures. Afterward (lines 3-5), we initialize S as an empty list and

draw a random seed that is then used to invoke the abstract function init _ noise _ sampler , which returns a noise sampler that provides a reproducible random path for the backpropagation phase (see §3.2). After the input is diffused (lines 6-8) via eq. (2) , lines 9-15 correspond to the reverse pass: At each step t (effectively i ), ˆ x (that now represents ˆ x p t q ) is first appended to S , which will eventually contain all such intermediate outputs (line 10). The noise provided by NS for the current step i is then retrieved (line 11) and used to compute d ˆ x (line 12). d ˆ x is then added to ˆ x so that its current value becomes ˆ x p t ` dt q . This repeats until ˆ x ' ˆ x p 0 q . Unlike the naive implementation, we only store the intermediate results. For efficiency, we also avoid saving the random noise for each step i but utilize NS to reproduce those variables on demand. Before termination, we re-enable dependency storage (line 16) to ensure our code does not interfere with the execution of any other modules. Finally, ˆ x p 0 q is returned together with the state S and the sampler NS , which are stored internally for reproducibility during backpropagation.

DBP Parallelism. Although Algorithm 1 is presented for a single purification path, DiffGrad natively supports parallel purification of N stochastic copies to potentially obtain a significant speedup when computing higher-quality EOT gradients-see §3.2. For simplicity, we abstracted away the batch logic in the pseudo-code. In practice, prior to line 1, the input x is replicated N times ( N is an additional argument that can be provided to Algorithm 1). Line 4 returns N random seeds, and the resulting sampler NS manages N reproducible random paths. Line 7 draws N distinct noise samples to generate N diffused versions of x , and all subsequent steps operate copy-wise in parallel across these N instances.

Backpropagation. DiffGrad 's backpropagation logic is in Algorithm 2. Similar to earlier, red text refers to operations that deviate from traditional backpropagation, while blue lines are optional (guidance-related). In addition to the usual gradient grad w.r.t. ˆ x p 0 q , the inputs include multiple parameters normally exclusive to forward propagation, as they are required to re-calculate the dependencies. Additionally, the algorithm accepts the saved state S , and the same noise sampler NS to retrieve the stochastic path of the forward propagation. Before providing details, we note that by definition @ A , B P R d , it holds that:

where d denotes the element-wise product. Therefore, in order to calculate the gradients w.r.t. ˆ x p t q and guide as described in eq. (6) and eq. (9) , we may define an objective at each step t as:

and take its gradient w.r.t. the two elements of interest above, which explains the steps in our pseudo-code in Algorithm 2.

The procedure begins by creating a variable g _ grad and setting it to 0 (line 2). This will later be used to store the guidance gradients (see Appendix D.1.4). For each time step t (i.e., step i ), starting from t 1 ' ´ dt ( i ' 1 ), the process (lines 3-14) first retrieves ˆ x p t q from the saved state S (line 4) and the corresponding random noise for that step used during forward propagation (line 5) and computes ˆ x p t ` dt q , denoted as ˆ x ` dt (lines 7-9). Importantly, these computations are performed while storing graph dependencies (enabled on line 6 and re-disabled on line 11 to restore the normal execution state). Specifically, during the first step, we calculate ˆ x p 0 q from ˆ x p´ dt q . Afterward, we compute the objective Obj t (line 10) following eq. (12) that allows us to back-propagate the gradient from ˆ x p 0 q to ˆ x p´ dt q and guide using the stored dependencies, as per eq. (6) and eq. (9) . grad is then updated to hold the gradient of the loss function w.r.t. ˆ x p´ dt q as desired (line 12), and the gradient of guide due to this guidance path (i.e., from guide to the loss due to guide participating directly in the calculation of ˆ x p t ` dt q -see Appendix D.1.4) is added to g _ grad (line 13). This process repeats until grad finally holds the gradient w.r.t. ˆ x p t ˚ q and g _ grad holds the sum of gradients due to all guidance paths w.r.t. guide ( eq. (10) ). Note that after the required gradients w.r.t. ˆ x p t q and guide are obtained at each step, the dependencies are no longer needed and can be discarded. This is where our approach differs from traditional backpropagation algorithms, enabling memory-efficient gradient calculations (at the cost of an additional forward propagation in total). At this point (line 14), we have the gradient ∇ ˆ x p t ˚ q F and all is required is to use it to calculate ∇ x F , which is trivial

Require: Loss gradient grad w.r.t ˆ x 0 , Sample x , Score model s θ , Optimal diffusion time t ˚ , step size dt , Noise scheduler β , Reverse diffusion function calc _ dx , State S ' t ˆ x p dt ˚ i q| i P r r| t ˚ dt |s su Noise sampler NS , Auxiliary guidance input guide , Guidance function g , Guidance scale s

due to the chain rule since the closed-form solution for ˆ x p t ˚ q ' x p t ˚ q from eq. (2) indicates that this is equivalent to ∇ x F ' a α p t ˚ q ˚ p ∇ x p t ˚ q F q as we compute on line 16. We then calculate the guidance paths' gradient w.r.t x following eq. (11) on line 17. Finally, we sum both components, returning the precise full gradient w.r.t. x .

DBP Parallelism. Algorithm 2 is written for a single purified copy but in practice operates over a batch of N stochastic instances like Algorithm 1. As the forward pass stores N trajectories, the backward pass propagates gradients independently for each. The operations in the pseudo-code are thus applied copy-wise in parallel across all N instances. Finally, after line 18, the N gradients are averaged, yielding the EOT gradient.

D.4 Verifying the Correctness of DiffGrad

To ensure the correctness of DiffGrad , all that is required is to verify that each ˆ x p t ` dt q computed during backpropagation (line 9 in Algorithm 2) exactly matches the corresponding forward-computed ˆ x p t ` dt q (line 14 in Algorithm 1). This equality guarantees that the reconstructed computation graph faithfully mirrors the one produced by standard autodiff engines during their normal (noncheckpointed) operation, ensuring exact gradient recovery since we use them to perform the necessary backpropagation between each ˆ x p t ` dt q and ˆ x p t q .

Since our forward pass explicitly stores all intermediate states in S , we compare each recomputed ˆ x p t ` dt q with its forward counterpart during backpropagation. An exact match confirms that the system is computing precise gradients. We manually validated this for all timesteps.

For guidance gradients, correctness follows from the derivations in Appendix D.1.4. Once incorporated, the same matching procedure ensures their correctness as well.

E Additional Details on Systems & Models

WideResNet-28-10 and WideResNet-70-16 [52] are used for CIFAR-10 , and ResNet-50 [18], WideResNet-50-2, and DeiT-S [14] for ImageNet , similar to [30, 20]. For VP-SDE DBP ( DiffPure ) [30], the DM s [12, 36] are those from the original work. We also experiment with the Guided -DDPM (see §3.2), GDMP [40], due to its SOTA robustness, using the author-evaluated

DM s [12, 19]. The settings match the original optimal setup [40, 30]: For Diffpure , t ˚ ' 0 . 1 for CIFAR-10 and t ˚ ' 0 . 15 for ImageNet . For GDMP , a CIFAR-10 sample is purified m ' 4 times, with each iteration running for 36 steps ( t ˚ ' 0 . 036 ), using MSE guidance [40]. ImageNet uses 45 steps ( m ' 1 ) under DDPM -acceleration [12] with SSIM guidance [43].

F One-Shot DBP Baseline Comparisons Against DiffGrad's Accurate Gradients

As noted in §3, DBP 's robustness stems from two sources: inaccurate gradients and improper evaluation. As our work offers enhancements on both fronts, we evaluate each factor separately. Here, we isolate the gradient issue by re-running prior experiments under the same one-shot evaluation protocol, but with accurate gradients via our DiffGrad module and compare the results to those from the literature. We restrict our attacks to 10 optimization steps (with AA -ℓ 8 ), while prior works often use up to 100 , giving them a clear advantage. We evaluate on CIFAR-10 with WideResNet-28-10, using N ' 128 EOT samples as justified in §3.2. For papers reporting several results, we chose their best.

Baselines. To demonstrate the efficacy of exact full gradients, we compare our DiffGrad module against prior gradient approaches. For DiffPure , the adjoint method was originally used [30], while GDMP was initially evaluated using BPDA [2] and a blind variant (ignoring the defense entirely) in Wang et al. [40]. These approximations were later criticized for poor attack performance [41, 26, 20, 24]. More recently, Lee and Kim [24] proposed the surrogate process to approximate the gradients, performing the reverse pass with fewer steps during backpropagation to reduce memory usage, enabling approximate gradients via standard autodiff tools. DiffAttack [20], DiffHammer [41], and Liu et al. [26] proposed checkpointing for memory-efficient full-gradient backpropagation. However, DiffHammer avoids the standard one-shot evaluation (1-evaluation) protocol and reports no results under it, while DiffAttack does not evaluate GDMP and continues to use the adjoint method for DiffPure . We focus here on existing results under the 1-evaluation protocol and defer the discussion of these works' conceptual issues (see §1) to §4.2.

Metric. Following prior works, we report robust accuracy ( Rob-Acc ): the fraction of samples correctly classified after the attack completes and the final adversarial example is purified and evaluated (once).

Results. Table 4 shows our comparison. All methods achieve similar clean accuracy (Cl-Acc) without attacks, with minor variation due to sample selection. Thus, robust accuracy (Rob-Acc) differences reflect the effect of gradient methods. Full denotes the standard AA attack that uses the full exact gradients (i.e., via checkpointing).

Our approach significantly outperforms gradient approximations such as Adjoint , Blind , and BPDA , reaffirming their known weaknesses. More notably, despite using only 10 optimization steps, our method reduces DiffPure 's Rob-Acc by 14 . 06% compared to Liu et al. [26], who also use exact gradients, confirming their backpropagation mismatches (see §3.2).

While DiffAttack remains slightly stronger, the difference is extremely small ( 1 . 4% ) and can be safely attributed to differing evaluation samples. Importantly, the original gap reported in Kang et al. [20] between DiffAttack and the standard AA -ℓ 8 dropped by 23 . 76% , undermining its claimed advantage due to the per-step deviated reconstruction losses and aligning with our theoretical findings in §3.1. As DiffAttack involves broader architectural changes beyond gradient logic, we provide detailed comparisons in §4.2, where we clearly showcase its inferiority.

Our method also slightly outperforms Surrogate for DiffPure ( 0 . 23% ), but we caution against overinterpreting this small gap: under the improper one-shot evaluation, several purification paths can

Table 4: One-shot AA -ℓ 8 comparison on CIFAR-10 ( ϵ 8 ' 8 { 255 ). : indicates strategy is PGD .

still cause misclassification even if the majority yield correct labels. As such, good approximation methods like Surrogate may appear closer in performance than they truly are. To verify the superiority of our DiffGrad 's full gradients over the surrogate approximation against DiffPure , we thus further compare the two under the realistic MV protocol studied in §4.2, executing AA -ℓ 8 with the surrogate process to obtain the gradients when attacking the same CIFAR-10 classifier considered in §4.2 (i.e., WideResNet-70-16) and using the same number of samples ( N ' 10 ) over which the majority vote is taken. We find that the surrogate process brings MV.Rob to 43 . 75% only, whereas our Full -DiffGrad lowers this number to 39 . 45% , achieving a considerable improvement of 4 . 3% and unequivocally proving the advantage of exact gradient computations. Finally, for GDMP , our method outperforms Surrogate by 5% even in the one-shot evaluation protocol (see Table 4), largely due to our incorporation of guidance gradients-entirely absent in all prior approaches-highlighting the unique strength of DiffGrad .

Note that the surrogate method shortens the trajectory and backpropagates through this shorter horizon but retains the full graph over that path. Hence, one may argue that the attack success degradation is an acceptable tradeoff when using the surrogate method given the potential speedup. Yet, in DBP , memory-not FLOPs-is the bottleneck; Checkpointing (e.g., our DiffGrad ) recomputes individual path segments, yielding exact gradients with lower peak memory. The surrogate may improve speed but not memory pressure, and its truncation can miss dependencies, weakening gradients as shown above. In practice, attackers precompute adversarial examples offline since DBP 's latency makes real-time adversarial generation infeasible either way, so runtime savings alone do not translate to a practical advantage.

All in all, the results demonstrate the fragility of DBP in the face of accurate gradients and highlight the issues in previous works' backpropagation. Nonetheless, this one-shot evaluation protocol remains problematic, as previously stated, leading to an inflated robustness estimate. In fact, under more realistic settings (see §4.2), we demonstrate that this gradient-based attack almost entirely defeats DBP when only one sample is used to predict the label (i.e., Wor.Rob).

G Evaluations with Liu et al. [26]'s Fixed AutoAttack

Liu et al. [26], like DiffHammer [41] and our own analysis, note that evaluating a single purification at attack termination inflates robustness scores. Liu et al. [26] address this by evaluating 20 replicas of the final AE , declaring success if any is misclassified. While similar in spirit to the Wor.Rob metric we consider

(see §3.3), this protocol is more limited: it evaluates only at the final step, whereas Wor.Rob evaluates N copies at each attack iteration. Accordingly, Liu et al. [26] group their method with one-shot evaluations, providing a slightly more realistic assessment

that leads to results similar to those attained via PGD [23].

We replicate their setup using DiffGrad (Table 5), running 20 iterations with N ' 10 EOT samples per step and evaluating 20 final replicas. Under this protocol, our improvements are stark. On WideResNet-28-10, we reduce Rob-Acc by 25 . 39% and 30 . 42% for DiffPure and GDMP , bringing final accuracy to 30 . 86% and 10 . 55% , respectively. These results confirm the superiority of DiffGrad 's gradients and expose DBP 's realistic vulnerability. We observe similar results on WideResNet-70-16 (not evaluated in [26]).

H Ablation Study with Different Numbers of Samples for Label Prediction

To assess the impact of the number of evaluation samples N , we test both single-purification and majority-vote (MV) settings with N P t 1 , 10 , 128 u . Our goal is to highlight the brittleness of DBP 's standard deployment, which classifies based on a single purified copy. As explained in §3.3, in

stateless setups (e.g., phishing, spam, CSAM), adversaries can resubmit identical queries indefinitely. Since randomized defenses like DBP can fail along certain stochastic paths, any non-negligible misclassification probability compounds with repeated attempts-see §3.3. Although DBP assumes this probability is negligible, our proof in §3.1, results in §4, and the ablation experiments here contradict this. Furthermore, we wish to showcase the advantages of our proposed majority-vote (MV) setting that strives to mitigate this vulnerability by, instead, classifying based on expectation of the randomized defense.

We evaluate DiffPure and GDMP on CIFAR-10 using WideResNet-70-16 and (our) AA -ℓ 8 (with ϵ ' 8 { 255 and 100 iterations). For N ' 1 and N ' 10 , we use 10 EOT samples; for N ' 128 , we reuse the same 128 samples for both EOT and evaluation. This improves gradient quality, thus strengthening attacks, yet still leads to higher MV robustness, proving the superiority of our proposed method despite the use of more accurate gradients.

For Wor.Rob, clean accuracy (Cl-Acc) remains constant across all N values since we always compute it using a single purified copy ( N ' 1 ), independent of the number N of samples used in the attack. This reflects the actual standard single-purification deployment of DBP , where the defender classifies a single output, while the attacker may retry multiple times. Hence, for Rob-Acc we consider a batch of multiple samples (the corresponding N in that row) and then declare attack success if a single misclassification occurs, revealing the gap between measured and effective robustness. In contrast, MV.Rob clean accuracy varies with N , as the prediction always aggregates over N purified samples, consistent with our proposed deployment.

Table 6 confirms that Wor.Rob consistently declines with N , revealing the illusion of robustness under single evaluation. For instance, DiffPure shows a drop from 35 . 16% (at N ' 1 ) to 17 . 58% at N ' 128 (far lower than the inflated numbers reported in previous studies-see Appendix F), confirming that many stochastic paths yield incorrect predictions, as our properly implemented gradient-based

attack (see §3.2) lowers the expected classification confidence, making such failure modes more likely. For GDMP , we observe a similar trend.

In contrast, MV.Rob improves with N , rising from 35 . 16% to 47 . 72% for DiffPure , and from 8 . 59% to 32 . 81% for GDMP . This affirms MV as a more stable and accurate evaluation method that must be adopted as the de facto standard for DBP evaluations in the future.

Yet, despite MV 's benefits, our gradient-based AA -ℓ 8 attack still degrades robustness, which never exceeds 50% , validating our theoretical finding from §3.1 that such attacks repurpose DBP into an adversarial distribution generator.

Computational Cost. While larger N increases computational overhead, we identify N ' 128 as the max batch size fitting in a single A100 GPU run requiring ' 26 . 53 s for inference, with N ' 10 offering a practical middle ground ( 6 . 54 s vs. 5 . 29 s for N ' 1 ). Hence, for practicality and if throughput is critical, one should opt for N ' 10 . However, in security-critical systems where latency is not crucial, a larger N is favorable. Yet, additional tests (not shown) suggest MV.Rob plateaus near N ' 128 . Note that these latencies refer to purification inference alone (classification excluded). During attacks (not standard deployment), there is also the cost of backpropagation. When accounting for the cost of classification and backpropagation, the latency becomes ' 17 s for N ' 1 and N ' 10 compared to ' 53 s for N ' 128 . As explained in §3.2, our design allows purifying multiple stochastic copies of the same sample in one step, in contrast to previous work. This reduces the runtime per EOT gradient from up to N ˆ 17 s-where N stochastic purifications are run serially-to just T N s, where T N is the latency incurred by purifying N samples in a batch, yielding a speedup of up to N ˆ 17 { T N for single-sample attacks, which amounts to 41 . 06 ˆ for N ' 128 allowing for a considerable speedup when the objective is to utilize many EOT samples to obtain accurate gradient estimates. For batch attacks, prior methods purify one stochastic copy per sample per EOT step and require all samples to converge before proceeding to the next batch of

inputs, blocking early termination. In contrast, DiffGrad purifies N copies of a single sample in parallel, allowing samples to terminate independently. This greatly improves overall throughput by freeing compute sooner, especially when convergence varies across inputs.

ImageNet timings: While we limit our ablation studies to CIFAR-10 for feasibility, we provide ImageNet timings for completeness. At ImageNet resolution on a 40 GB A100 GPU, DBP inference (forward propagation only) requires ' 7 s for N ' 1 and ' 25 s for N ' 8 . A single attack iteration (i.e., forward and backward propagation) lasts ' 16 s ( N ' 1 ) and ' 75 s ( N ' 8 ). Thus, batching EOT copies yields a significant speedup over serial purification for both attacks and inference, but models and activations dominate cost at this scale, so batching returns diminish faster than on CIFAR-10 .

Recommendations for Choosing The Batch Size N . We found N ' 128 for CIFAR-10 and N ' 8 for ImageNet to be the largest feasible batch sizes to fit into the 40 GB A100 GPU memory, making larger batches impractical for large-scale evaluations. That said, control experiments with larger N values for both datasets (split into batches) showed negligible robustness or attack performance gains, indicating saturation.

Following the above discussion, we recommend N ' 10 for CIFAR-10 as a practical default and N ' 64 ´ 128 for security-critical inference ( MV ) and highly accurate gradients when evaluating new attack methods such as our LF strategy-see §5. For ImageNet , we recommend N ' 8 for similar reasons; larger N values remain preferable when added latency is acceptable.

I Details on Our Low-Frequency ( LF ) Adversarial Optimization Strategy

I.1 Understanding Optimizable Filters

In practice, OFs extend an advanced class of filters, namely guided filters, that improve upon the basic filters discussed in §5. Guided filters employ additional per-pixel color kernels that modulate the distortion at critical points: Since filters interpolate each pixel with its neighbors, they are destructive at edges (intersections between different objects in the image), while the values of non-edge pixels are similar to their neighbors, making such operations of little effect on them. Depending on a permissiveness σ , guided filters construct, for each pixel p i, j q a color kernel C i,j x ,σ c of the same dimensionality M ˆ N as K that assigns a multiplier for each of p i, j q 's neighbors, that decays with the neighbor's difference in value from p i, j q 's. The output at p i, j q involves calculating the effective kernel V i,j x , K ,σ c ' C i,j x ,σ c d K (normalized) which then multiplies p i, j q 's vicinity, taking the sum of this product. Thus, contributions from neighbors whose values differ significantly are diminished, better preserving information.

Guided filters still employ the same K for all pixels, changing only the color kernel that is computed similarly for all pixels. Thus, to incur sufficient changes, they would also require destructive parameters despite them still potentially performing better compared to their pristine counterparts. Their parameters are also predetermined, making it impossible to optimize them for a specific purpose. The OFs by Kassis and Hengartner [21] build upon guided filters but differ in two ways: First, instead of using the same K , they allow each pixel to have its own kernel K i,j to better control the filtering effects at each point, ensuring visual constraints are enforced based on each pixel's visual importance. In this setting, K ˚ denotes the set including all the per-pixel kernels K i,j . Second, the parameters θ K ˚ of each filter are learnable using feedback from a perceptual metric ( lpips ) [56] that models the human vision, leading to an optimal assignment that ensures similarity while maximizing the destruction at visually non-critical regions. To further guarantee visual similarity, they also include color kernels similar to guided filters (see original paper for details [21]).

I.2 Attack Hyperparameters

Through experimentation, we found that the loss balancing constants c ' 10 8 for CIFAR-10 and c ' 10 4 for ImageNet lead to the fastest convergence rates and selected these values accordingly (although other choices are also possible). UnMarker 's filter network architecture for ImageNet is identical to that from the original paper [21]. For CIFAR-10 , since the images are much smaller, we found the original architecture unnecessarily costly and often prevents convergence since larger filters group pixels from distant regions together in this case, easily violating visual constraints upon each

update, resulting in the lpips condition being violated. Thus, we opt for a more compact network that includes filters with smaller dimensions, which was chosen based on similar considerations to [21], allowing us to explore several interpolation options. The chosen architecture for CIFAR-10 includes 4 filters, whose dimensions are: p 5 , 5 q , p 7 , 7 q , p 5 , 5 q , p 3 , 3 q . We use fixed learning rates of 0 . 008 for the direct modifier δ and 0 . 05 for the filters' weights, optimized using Adam . The remaining hyperparameters were left unchanged compared to [21].

I.3 Pseudo-Code

The pseudo-code for our low-frequency ( LF ) strategy (see §5) is in Algorithm 3. Importantly, as each K i,j b 's values should be non-negative and sum to 1 , the values for each such per-pixel kernel are effectively obtained by softmax ing the learned weights. Initially, the modifier ˆ δ is initialized to 0 and the weights t p θ K ˚ b u are selected s.t. the filters perform the identity function (line 1). As a result, the attack starts with x adv ' x that is iteratively optimized. Similar to C&W [4], we directly optimize x adv (i.e., using the modifier ˆ δ ) in the arctanh space, meaning we transform the sample first to this space by applying arctanh (after scaling x adv to arctanh 's valid range r´ 1 , 1 s ) where ˆ δ is added and then restore the outcome to the original problem space (i.e., r min _ val, max _ val s , which is typically r 0 , 1 s ) via the tanh operation. Further details on this method and its benefits can be found in [4]. All other steps correspond to the description brought in §5. Unlike §3.1, we assume the classifier M outputs the logit vector rather than the probabilities (i.e., we omit the softmax layer over its output, which me or may not be re-introduced by the loss ℓ ), as is traditionally done for a variety of adversarial optimization strategies (e.g., C&W [4]) to avoid gradient vanishing. We use the known max-margin loss [4]ℓ p logits , y q' logits r , : y s´ max j ‰ y t logits r , : j su .

Algorithm 3 Low-Frequency ( LF ) Adversarial Optimization

To average the gradients over multiple ( N ) paths as per the adaptive attack's requirements from §3.1, we generate several purified copies by repeating the sample x adv under optimization n times before feeding it into the DBP pipeline (line 9). Here, n corresponds to the maximum number of copies we can fit into the GPU 's memory during a single run. However, as this n may be smaller than the desired N from §3.1 (i.e., number of EoT samples) that allows us to sufficiently eliminate the error in the computed gradient, we use gradient accumulation by only making updates to the optimizable parameters (and then resetting their gradients) every eot _ steps iterations (lines 16-19). By doing so, the effective number of used copies becomes n ˚ eot _ steps , which can represent any N of choice that is divisible by n . Note that if n is not a divisor of N , we can always increase N until this condition is met, as a larger N can only enhance the accuracy). This also explains why the algorithm runs for max _ iters ˚ eot _ steps (line 5).

Finally, the condition Cond captures the threat model (either SP or MV -see §2): When the logits for the batch of n copies are available together with the target label y , Cond outputs a success decision based on whether we seek misclassification for the majority of these purified copies or a single copy only. Note that, as explained in §4.2, we take the majority vote over the maximum number of copies we can fit into the GPU (i.e., n ) for MV . As this choice was only made for practical considerations, one may desire to experiment with different configurations wherein another number of copies is used. Yet, this is easily achievable by simply modifying Cond accordingly: For instance, we may augment it with a history that saves the output logits over all eot _ steps (during which x adv is not updated). Then, the majority vote can be taken over all copies in this window. Note that by increasing the number of eot _ steps , we can use as many copies for the majority vote decision as desired in this case. That said, the attack will become significantly slower.

In addition to the precise gradient module DiffGrad , our DiffBreak toolkit provides the implementation of our LF strategy as well as various other common methods (e.g., AA and StAdv ), to enable robust and reliable evaluations of DBP . All strategies are optimized for performance to speed up computations via various techniques such as just-in-time ( JIT ) compilation. Our code is available at https://github.com/andrekassis/DiffBreak .

J Example Attack Images

In Appendix J.1-J.10, we provide a variety of successful attack images that cause misclassification in the rigorous MV setting, generated using our low-frequency ( LF ) strategy against all systems considered in §5.1. For configurations that were also evaluated against AA -ℓ 8 under the same MV setting (i.e., using the same sample counts N as used for LF in §5.1), we include successful AE s generated with this method for direct comparison. Specifically, for ImageNet , both the LF attack in §5.1 and the AA attack in §4.2 were evaluated under MV with N ' 8 ; hence, we include AA samples for ImageNet directly from §4.2. For CIFAR-10 , the AA experiments in §4.2 use the more permissive N ' 10 setting. Therefore, we instead draw samples from the corresponding N ' 128 AA experiments reported in Appendix H to ensure a fair comparison under equal majority-vote conditions. Note that all samples are crafted using the parameters listed in §4.2 and §5.1. That is, τ p ' 0 . 05 for LF and ϵ 8 ' 8 { 255 for AA against CIFAR-10 and ϵ 8 ' 4 { 255 against ImageNet .

For the configurations that were evaluated against both strategies, we provide two sets of samples: 1) Three triplets containing the original image, the AE generated using AA , and the AE crafted using LF . Importantly, all original samples in this set are inputs for which both methods can generate successful AE s, and we provide these to allow for a direct comparison between the two strategies' output quality on a sample-by-sample basis. Yet, as AA is inferior to our approach ( LF ), resulting in the systems retaining robustness on many inputs for which it fails to generate successful AE s under MV , it is essential to inspect LF 's outputs on such more challenging samples to demonstrate that it still preserves quality despite its ability to fool the target classifiers. Thus, we include a second set of 2) Three successful AE s generated with LF from inputs on which AA fails under MV . For the remaining configurations that were not evaluated against AA under the same MV sample counts from §5.1, we provide six successful AE s generated with LF .

In Appendix J.11, we present attack images generated by the non-norm-bounded StAdv [47] strategy under MV (with the above sample counts N ). This method has demonstrated superior performance to norm-based techniques in the past against DBP [30] even in the absence of the correct exact gradients, indicating it could be a viable attack strategy with our gradient computation fixes, thereby making

our LF approach unnecessary. Yet, previous evaluations only considered StAdv against DBP for CIFAR-10 [30]. While we find StAdv capable of defeating all systems (for both CIFAR-10 and ImageNet ), it leads to severe quality degradation when used to attack DBP -protected classifiers for high-resolution inputs (i.e., ImageNet ), leaving the AE s of no utility. Thus, we deem it unsuitable, excluding it from the main body of the paper accordingly. Further details are in Appendix J.11.

All samples below are originally (without adversarial perturbations) correctly classified.

J.1 Attack Samples Generated Against CIFAR-10 's WideResNet-70-16 with GDMP Purification

4

J.2 Attack Samples Generated Against CIFAR-10 's WideResNet-28-10 with GDMP Purification

Note: While WideResNet-28-10 was not evaluated against AA under MV with N ' 128 in Appendix H, we include AA samples here to complement our CIFAR-10 analyses-our primary benchmark for AA-based evaluation. Among the two main purification paradigms considered (GDMP and DiffPure), we randomly selected GDMP for this illustrative example.

J.3 Attack Samples Generated Against CIFAR-10 's WideResNet-70-16 with DiffPure Purification

J.4 Attack Samples Generated Against CIFAR-10 's WideResNet-28-10 with DiffPure Purification

J.5 Attack Samples Generated Against ImageNet 's DeiT-S with GDMP Purification

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J.6 Attack Samples Generated Against ImageNet 's WideResNet-50-2 with GDMP Purification

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J.7 Attack Samples Generated Against ImageNet 's ResNet-50 with GDMP Purification

J.8 Attack Samples Generated Against ImageNet 's DeiT-S with DiffPure Purification

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J.9 Attack Samples Generated Against ImageNet 's WideResNet-50-2 with DiffPure Purification

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ukaths

J.11 Quality Comparison with StAdv

We found StAdv capable of generating outputs that defeat DBP even under MV . However, it is not suitable for targeting DBP -defended classifiers that operate on high-resolution images. The reason is that StAdv performs spatial transformations that relocate the different pixels. Thus, its changes quickly become visible when applied excessively. Due to the considerable stochasticity of DBP (see §4.2), the required displacements (especially in the MV setting) are significant, which in turn can severely impact the quality. For low-resolution inputs (e.g., CIFAR-10 ), StAdv can still be effective, with the quality degradation remaining unnoticeable due to the size of the images that renders them blurry by default, masking StAdv 's effects. For high-resolution inputs, the degradation is substantial, leaving the outputs useless as stealthiness is a key requirement from practical AE s [21]. StAdv 's successfully misclassified samples (under MV ) below prove these claims. We use Full-DiffGrad for backpropagation and run StAdv with its default parameters [47]. When the parameters are changed to better retain quality, StAdv ceases to converge for ImageNet , making it of no use. All provided samples are originally correctly classified.

TURN

rchitectureTechnologyUserNetwork

Peer reviews:
comments: SUMMARY:
This paper attempts to break diffusion based adversarial defenses empirically with (1) improved implementation details (2) additional techniques like LF. The authors present siginificant vulnerabilities in the DBP methods.

STRENGTHS AND WEAKNESSES:
Strength
1. I believe this paper conveys a very strong and impactful message to the community by exposing the vulnerability of diffusion based defenses. DBP methods have been widely studied and are considered promising given their effciency compared to AT. However, if all the previous success should be attributed to improper and inadaquate evaluation protocal, then it is of great importance to convey this to the reserach community.
2. The technical insights and implementation details are solid. 
3. The introduction of LF methods is novel and exhibits high effectiveness.

Weakness
Generally, there is no major technical flaws in this paper. There are two minor weakness from my standpoint.
1. I personally do not favor discussing much about Theorem 3.1, since both the theoretical result and the proof process are relatively intuitive. Clearly stating the reasons why the certifiable robustness of DBP might not realizable in practise is already a meaningful complement to related theoretical works.
2. The "Reproducing Stochasticity" assumption is valid for worse case evaluation. However, this might be a assumption too strong to hold in practise.

QUESTIONS:
Please see weakness.

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 4
IMPACT: 4
ORIGINALITY: 3
DATE: 2025-06-27

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper critically evaluates the popular diffusion-based purification (DBP) defense against adversarial examples and highlights the flaws in the existing approaches. The paper uses adaptive attacks to show that the robustness claimed by prior works is inflated due to the reliance of these defenses on flawed gradients. The paper then proposes a toolkit, DiffBreak, to eliminate the gradient flaws and curb the inflated robustness estimates. The paper also proposes a low-frequency attack inspired by [21] that further degrades the performance of the DBPs.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The paper highlights a new vulnerability of existing DBP-based defenses, as well as previous methods such as DiffusionHammer, which further reduce the robustness performance of DBP-based defenses. In particular, the paper’s insight that the use of accurate gradients for generating adversarial examples ends up using the purification process to the attacker’s advantage is critical.\n2. The paper proposed a toolkit that could be used by model builders to evaluate their models’ robustness to adversarial examples.\n3. The low-frequency adversarial examples while not novel, have been shown to be effective at bringing down the robustness of various models.\n4. The paper thoroughly evaluates various methods, including some recently proposed defenses, and highlights that their robustness is also flawed.\n\n\nWeaknesses/Questions\n\n1. The proposed Majority Voting (MV) based metric is weaker than the worst-case robustness metric proposed by [41]. What is the purpose of this new metric?\n2. The evaluation consists of very low-resolution data. Do the findings transfer to much larger image sizes?\n3. What is the computational complexity for computing an attack against DBP for higher resolution images?\n4. Are the proposed findings transferable to different modalities of data or limited to just images?\n\nQUESTIONS:\nSee above\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper challenges the robustness of diffusion-based purification (DBP) methods. This paper nullifies DBP’s core premise by proving that standard gradient-based attacks can manipulate the diffusion model’s score function to generate adversarial distributions rather than natural ones. To address these issues, this paper proposes DiffGrad, which is a reliable backpropagation toolkit for DBP that fixes gradient inaccuracies in prior works. Experiments show that DBP’s robustness drops significantly when using DiffGrad to calculate the gradients.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**:\n\n- This paper tackles a very important & interesting problem in DBP methods. Evaluation is a long-standing problem for DBP methods. Due to the computational cost of accessing Diffusion model’s gradient, many methods rely on inappropriate approximations of the gradients, which in general may lead to the overestimated robustness of DBP methods.\n- This paper is well-written and theoretically sound. The theoretical analysis proves DBP’s vulnerability to adaptive attacks.\n- Experiments are solid and sufficient.  The robustness of DBP methods drops significantly after applying DiffGrad.\n- The observation that the low-frequency AEs can beat both DBP and AT methods is interesting and surprising, especially for DBP methods since they do not implicitly make  assumptions on the types of incoming AEs.\n\n**Weaknesses**:\n\n- Experiments use a small test set (256 samples per dataset), which is not sufficient, although the setting aligns with previous work.\n- The core insight that attacks can exploit DBP’s stochasticity aligns with previous work (i.e., DiffHammer), though this work goes further with low-frequency attack.\n\nQUESTIONS:\nRegarding the future of adversarial purification, do you view diffusion models as a promising direction if further refined, or would you recommend exploring fundamentally different architectures beyond diffusion models? Looking forward, what key innovations would be needed to make diffusion models robust against adversarial attacks? Any discussion is appreciated.\n\nLIMITATIONS:\nYes, the authors provide a detailed discussion of limitations and broader impacts in Appendix A.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper argues that Diffusion-Based Purification (DBP), a defense against adversarial attacks, is not robust. The authors claim that attacks can manipulate the core diffusion model instead of just tricking the classifier. They introduce a toolkit called DiffBreak to show this, which includes a more accurate way to calculate attack gradients (DiffGrad) and a better evaluation method (Majority-Vote). They also propose a \"low-frequency\" attack that they claim breaks DBP completely.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- The paper points out that testing a randomized defense like DBP with just one try isn't reliable. Their proposed Majority-Vote (MV) method is a more common-sense approach to measuring robustness.\n- The DiffGrad module seems like a solid piece of engineering. It fixes several technical issues in previous attack implementations, which could help the research community conduct more reliable experiments in the future.\n- The authors test their claims across several standard datasets and models (CIFAR-10, ImageNet), which makes their empirical findings convincing.\n\nWeaknesses:  \n- The paper exhibits weaknesses in its treatment of prior work and internal consistency. It repeatedly characterizes methods like DiffHammer and DiffAttack as having \"flawed\" gradients, overlooking that approaches such as surrogate approximations represent intentional computational trade-offs rather than fundamental errors. For example, DiffHammer’s checkpointing balances memory efficiency against gradient precision, a reasonable engineering compromise.\n- The paper first evaluates DBP against standard, norm-bounded attacks and shows it still has some robustness. Then, it introduces a completely different type of attack (the \"LF attack\") which is not norm-bounded and uses it to declare that DBP is broken. This seems like shifting the evaluation criteria.\n\nQUESTIONS:\n- The LF attack uses LPIPS as a perceptual constraint. Have you experimented with other perceptual metrics, and do you believe the attack's success is specific to LPIPS or would generalize to other perceptual similarity measures?\n- Could the principle of implicitly optimizing the parameters of a pre-processing defense be generalized to other types of defenses that are often treated as fixed, such as JPEG compression or other input transformations? \n- The Majority-Vote protocol is a key contribution. The experiments use K=10 or K=8 samples. How was this number determined? Is there a performance/robustness trade-off curve as K increases, and what would be a practical recommendation for K in a real-world deployment?\n\nLIMITATIONS:\nThe authors admit their methods are very computationally expensive.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-05"}