{"id":"0c8d28ea-9578-409c-bca4-b8952f752032","arxiv_id":"2506.13834","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"A natural-evolution-strategy update for guided diffusion is derived and shown to match gradient guidance in a limiting case, then demonstrated on fluidic and meta-surface design using surrogate fitness models.","lead":"The paper replaces gradient-based guidance in diffusion models with an evolution-strategy update that uses only fitness evaluations, aiming to let non-differentiable physics solvers steer generation. It reports lower pressure-drop fluid channels and better meta-surface transmission profiles, but the experiments use learned surrogate evaluators rather than the actual physics solvers.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The core update evaluates final-design fitness on intermediate noised states without justification, so guidance may not optimize the stated objective; central claim unsupported.","rationale":"The reader's weakest_assumption identifies precisely the same load-bearing concern: fitness is evaluated on intermediate noised samples rather than final designs. My stress-test confirms this is the principal threat to the central claim. The derivation of the natural-gradient update itself is a standard evolution-strategy result; the issue is the objective mismatch between Eω[f(xt)] with intermediate xt and the final-design fitness f(x0). The paper's experiments do not resolve this: they use a regressor trained on clean x0 as the oracle, and no validation is provided that its outputs on noised samples correlate with true final-design fitness. This is not merely an empirical gap; it is a correctness risk in the algorithm's definition. There are secondary issues (the ||Σ||→0 reasoning in Proposition 1 is mathematically sloppy, and rank-based shaping changes the objective), but they are less central. Given that the core mechanism is unsupported and the reported results can be explained by the regressor's behavior on out-of-distribution inputs rather than by genuine optimization of the design objective, the evidence does not support the claim that the method enables guidance by non-differentiable multi-physics models. The verdict of REJECT remains appropriate.","tokens_in":12542,"tokens_out":7067,"duration_ms":69085,"concrete_test":"Using the pre-trained diffusion model and the regressor from Section 4.1, fix a denoising step t in the guided phase (e.g., t = 50). For 1000 random initial xT, draw the Ns=30 intermediate samples x_i_t from N(μθ(xt), Σθ(xt)). For each x_i_t, fully denoise it to a clean x0 (without guidance) and compute the true CFD pressure drop Δp_true(x0). Then compute the Spearman rank correlation between the regressor's predictions f(x_i_t) and Δp_true(x0). If the correlation is near zero or negative, the guidance signal in Algorithm 1 does not reflect the stated objective, confirming the concern. A secondary check: recompute the results of Figure 3 using fitness evaluated only on fully denoised x0 (by rolling out each sample to the end) and compare with the reported results; if there is a large divergence, the intermediate evaluation is the cause.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that pre-trained diffusion models can be guided by arbitrary black-box fitness functions defined on final designs. However, Algorithm 1 (lines 4–5) evaluates f on samples drawn from N(μθ(xt), Σθ(xt)), i.e., the denoising distribution for xt−1, which are partially noised states. The theoretical objective in Eq. (4) is instead J(ω) = Eω[f(xt)] with xt interpreted as an intermediate sample, but the actual design problem defines fitness on the fully denoised x0. The paper never justifies that a fitness function trained/evaluated on clean x0 yields meaningful values on partially denoised samples. In the experiments, a regressor trained on paired (x0, Δp) data is used as the oracle, so its outputs on noised intermediate samples are extrapolations outside the training distribution. If this mapping is unreliable, the natural-gradient estimate in Eq. (13d) is not estimating the gradient of the stated final-design objective; the guidance updates could steer the denoising process toward states that merely fool the regressor on noised inputs, without improving the actual design metric. This is load-bearing because every update step in Algorithm 1 depends on these intermediate fitness values. Without a noise-aware surrogate or an explicit mechanism to evaluate fitness on final designs, the method's effectiveness for black-box, non-differentiable solvers is not established; the proof of Proposition 1 only connects the update to gradient guidance when f is a function of the sampled xt, not when f is defined on x0.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes 'evolvable conditional diffusion,' a derivative-free guidance method for pre-trained diffusion models. The authors formulate guided denoising as maximizing an expected fitness under the Gaussian denoising distribution, derive a natural-evolution-strategy update for the denoising mean, and show that in a small-covariance limit this update resembles the standard classifier-guidance update. They validate the method on two AI-for-Science tasks: fluidic channel topology design and frequency-selective meta-surface design, using a learned regressor as a stand-in for the black-box fitness evaluator. The central claimed contribution is that black-box, non-differentiable physics solvers can guide diffusion generation without computing gradients.","tokens_in":12836,"tokens_out":8351,"duration_ms":82965,"significance":"If the central claim were established, the method would be a useful addition to guided diffusion: it would let pre-trained diffusion models be steered by arbitrary black-box fitness functions, which is relevant for scientific design problems where solvers are non-differentiable. The paper's derivation of the natural-gradient update is standard NES machinery and is internally consistent up to the Monte Carlo estimator; the authors also correctly note that the update itself never requires derivatives of the fitness function. However, the experimental protocol does not establish the claimed capability: fitness is evaluated on intermediate noisy samples even though the design objective is defined on final designs, and the reported success metric is computed by the same learned regressor that provides the guidance signal. These issues are load-bearing for the paper's main claim, so the current evidence is not convincing.","major_comments":[{"comment":"Algorithm 1 evaluates the fitness f on samples drawn from N(µθ(xt), Σθ(xt)), which are intermediate denoising candidates, but the design objective f is defined only on final designs x0 (e.g., Δp obtained from CFD). The regressor used in the experiments was trained on paired (x0, Δp) data, so its outputs on partially noised images are out-of-distribution extrapolations. The paper provides no argument, theoretical or empirical, that these intermediate fitness values are meaningful for the final-design objective. Consequently, Eq. (13d) is not an estimator of the gradient of E[f(x0)] with respect to the denoising distribution, and the guidance updates in Algorithm 1 may be optimizing an objective that is different from, and unvalidated against, the stated design goal.","section":"Sec. 3.3, Algorithm 1, lines 4-5; Sec. 4.1 Implementation Details"},{"comment":"The reported performance metrics (histograms of Δp and MAE, and the per-step curves in Figures 3, 5, 6, 8, 9) are computed with the same learned regressor that supplies the guidance signal. There is no independent validation against the true CFD solver (Eq. 16) or a full-wave electromagnetic simulator on the generated designs. Because the regressor is evaluated on partially denoised, out-of-distribution inputs during the guidance process, the empirical results may reflect artifacts of the regressor rather than genuine improvement in the physical design objective. The claim that the method works with black-box non-differentiable solvers is therefore not established by the current experiments; at minimum, a subset of generated designs should be re-evaluated with the actual solver.","section":"Sec. 4.1 and Sec. 4.2, Results"},{"comment":"The theoretical objective J(ω) = Eω[f(xt)] does not specify which random variable xt denotes. In Algorithm 1, the samples x_i_t are drawn from the denoising distribution for the next state xt−1, while the fitness f is ultimately a function of the final state x0. The paper never defines a time-dependent fitness, a noise-aware surrogate, or an aggregation over the remaining denoising trajectory. Without such a definition, the sequence of updates in Algorithm 1 is not a consistent optimization of the final-design objective. This is a second, theory-level manifestation of the mismatch identified above and should be resolved in the formulation itself, not only in the implementation.","section":"Sec. 3.1, Eq. (4); Sec. 3.3, Algorithm 1"},{"comment":"The claimed equivalence between the derived update and the gradient-based guidance update Eq. (3) is shown in the limit ||Σθ|| → 0, but the natural-gradient formula (10) uses F^{-1} = Σθ, and the Dirac-delta step leading from Eq. (11a) to Eq. (11b) is not made rigorous. More importantly, in the actual algorithm Σθ is the learned covariance of the denoising step and is not small, so Proposition 1 does not justify the finite-covariance update as an approximation to classifier guidance. The update is a legitimate NES step, but the paper's central 'analogous to gradient-based guidance' claim requires a different argument or a precise asymptotic statement with explicit error bounds.","section":"Sec. 3.1, Proposition 1"}],"minor_comments":[{"comment":"The notation x_i_t is confusing: samples drawn from N(µθ(xt), Σθ(xt)) are candidates for xt−1, not for xt. Please rename them (e.g., x_{t-1}^{(i)}) and align the notation in Eq. (13) and Figure 1.","section":"Sec. 3.3, Algorithm 1"},{"comment":"The rank-based fitness shaping replaces f by r, which depends on the whole population of samples. The Monte Carlo estimate in Eq. (13d) is therefore not the natural gradient of J(ω) = Eω[f(xt)] as derived; the paper should state explicitly that the objective is changed to a rank-transformed fitness and discuss the consequences for the equivalence in Proposition 1.","section":"Sec. 3.2, Eq. (14)"},{"comment":"The label 'CD-50-0' in Figure 6 denotes α = 50 with 10-step guidance, while Figure 3 uses 'CD-5-0' for α = 5 with 50-step guidance. The naming convention is easy to confuse; a table or consistent naming scheme would help.","section":"Sec. 4.1, Figure 6"},{"comment":"The phrase 'Δp is normalized by ln Δp/5' is unclear. Please specify the exact normalization formula and the reason for it.","section":"Sec. 4.1, Figure 3 caption"},{"comment":"The claim that the method 'eliminate[s] the need for any a priori surrogate model' is in direct tension with the experimental setup, which trains a regressor to provide the fitness evaluations. This tension should be reconciled in the text.","section":"Sec. 5, Discussion"},{"comment":"The caption refers to 'predicted transmission profiles.' Please clarify whether these are regressor outputs or full-wave solver outputs; if they are regressor outputs, this limitation should be stated explicitly.","section":"Sec. 4.2, Figure 10"}],"recommendation":"reject","confidential_remarks":"The motivating problem is strong and the natural-gradient derivation is clean, but the manuscript as written cannot execute its stated objective with a solver that only evaluates final designs: Algorithm 1 evaluates the fitness on intermediate noisy samples, and the experiments use the same regressor for both guidance and evaluation. These are not local presentation issues; they undermine the central claim. A revision would need to redesign the evaluation protocol (e.g., noise-aware surrogate or full denoising rollouts for each candidate), validate against true solvers, and reconcile the 'no surrogate' claim. As such, I recommend rejection in the current form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Let me give you the short version. The paper takes standard natural evolution strategies, applies them to the mean of the denoising Gaussian at each step, and shows (again) that the NES update reduces to classifier guidance in the zero-variance limit. That's a clean way to see derivative-free guidance, but it's not new in the sense that Shen et al. and Li et al. have already proposed derivative-free guidance for diffusion. What is new here is the specific framing and the two applications to fluidic topology and metasurface design.\n\nWhat the paper does well: Section 3's derivation is straightforward and correct. The Monte Carlo estimate of the natural gradient is the standard rank-based NES update. Proposition 1 is a known limiting argument, but it is clearly stated. The algorithm is simple to implement, and the two design problems are relevant to AI for Science.\n\nWhere it falls apart: the fitness function in the theory is defined on samples from the denoising distribution — that is, on noised intermediate states. But the actual design objectives (pressure drop, transmission error) are defined only on the final design x0. In the experiments, a regressor trained on clean x0–Δp pairs is used as the oracle, and Algorithm 1 evaluates that regressor on x_i_t drawn from N(mu_theta, Sigma_theta) at each step. Those are out-of-distribution inputs for the regressor, and the paper offers no justification that the regressor's predictions on noised samples are meaningful for the final-design objective. On top of that, the reported success metric is presumably computed with the same regressor, so the evaluation is self-referential. There is no external validation with the actual CFD or electromagnetic solver on a handful of final designs.\n\nThe zero-covariance equivalence in Proposition 1 is also somewhat beside the point: in that limit the population collapses and the NES update becomes exactly the gradient update, but the whole motivation is a finite-variance population that can explore without gradients. So the 'equivalence' doesn't tell you much about the practical behavior.\n\nNet: the paper has a clean algorithmic idea and a plausible motivation, but the experiments do not validate the claim that you can guide with an arbitrary black-box solver. To make the case, the authors would need either to train a noise-aware surrogate (e.g., a classifier trained on noised inputs as in standard classifier guidance) or to evaluate final designs by calling the actual solver during guidance, which is expensive but feasible at small scale. As is, the central claim is not established.\n\nI'd send it to peer review, but the referee should insist on fixing the intermediate-sample evaluation problem and adding external validation. It's a borderline paper; the idea is worth engaging with, but the current evidence doesn't support the headline claim.","headline":"Clean NES-based derivation for diffusion guidance, but the experiments validate with the same surrogate that evaluates noised intermediate samples — so the black-box claim isn't actually shown.","tokens_in":13390,"tokens_out":2947,"would_cite":false,"duration_ms":27847,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper derives a derivative-free guidance update for diffusion models that matches gradient-based guidance in the small-covariance limit, enabling black-box fitness functions to steer generation.","keywords":["diffusion models","guidance","evolution strategies","natural gradients","black-box optimization","inverse design","rank-based fitness shaping","generative design"],"falsifier":"On a task with a known fitness function, compute the correlation between $f(x_t)$ at the guidance steps used by the algorithm and $f(x_0)$ for samples from the unconditional model; if the correlation is near zero or negative while the method still reports improvement, the improvement must come from something other than the claimed evolutionary objective, and if the correlation is low the method should fail when guidance is restricted to early, high-noise steps.","tokens_in":12349,"feed_emoji":"🎯","tokens_out":7111,"duration_ms":61556,"temperature":0.7,"pith_summary":"This paper claims that a pre-trained diffusion model can be guided toward designs that maximize an arbitrary black-box fitness function without ever computing a derivative. It derives an update to the mean of each denoising Gaussian by maximizing expected fitness under the current distribution, using the natural gradient of that expectation. In the limit where the covariance of the denoising distribution collapses, the natural gradient reduces to $\\Sigma_\\theta \\nabla_{x_t} f(x_t)$, the same direction used in standard gradient-guided diffusion. The paper then estimates this direction with Monte Carlo samples and rank-based fitness shaping, so the only requirement is the ability to evaluate fitness on samples. If correct, this turns non-differentiable physics simulators into usable guidance signals for generative design.","feed_headline":"No-derivative guidance now matches gradient-guided diffusion","feed_subtitle":"Rank-based fitness updates steer pre-trained diffusion with black-box solvers, no derivatives.","key_machinery":"The load-bearing identity is the natural-gradient expression for expected fitness under a Gaussian population model: with $p(x_t|\\omega)=\\mathcal{N}(x_t;\\mu_\\theta,\\Sigma_\\theta)$, the Fisher information matrix for $\\mu_\\theta$ is $\\Sigma_\\theta^{-1}$, so $\\tilde{\\nabla}_{\\mu_\\theta}J(\\omega)=\\Sigma_\\theta \\nabla_{\\mu_\\theta}\\mathbb{E}_\\omega[f(x_t)]$. The log-likelihood trick rewrites the gradient of the expectation as an expectation involving $\\nabla_{\\mu_\\theta}\\log p(x_t|\\omega)$, leading to the sample estimate $\\frac{1}{N_s}\\sum_i r(x_t^i)(x_t^i-\\mu_\\theta)$. Rank-based fitness shaping, replacing raw fitness $f$ with $r(x_t)=a+b\\,\\mathrm{rank}(f(x_t))$, makes the estimate invariant to order-preserving transformations of the objective and reduces sensitivity to extreme values.","core_discovery":"The central claim is that guidance in a diffusion model can be reformulated as an evolutionary optimization problem over the parameters $\\omega=(\\mu_\\theta,\\Sigma_\\theta)$ of the denoising Gaussian, with objective $J(\\omega)=\\mathbb{E}_\\omega[f(x_t)]$. Maximizing $J$ by a natural-gradient step yields the update $\\mu_\\theta^c=\\mu_\\theta+\\alpha\\tilde{\\nabla}_{\\mu_\\theta}J(\\omega)$, and when $\\|\\Sigma_\\theta\\|\\to 0$ the natural gradient equals $\\Sigma_\\theta\\nabla_{x_t}f(x_t)$, exactly the gradient-guidance update used in classifier-guided diffusion. The derivative-free version replaces the gradient with a Monte Carlo estimate $\\frac{1}{N_s}\\sum_i r(x_t^i)(x_t^i-\\mu_\\theta)$ obtained from samples drawn from the denoising distribution and their rank-shaped fitness values, so no differentiation of $f$ is ever needed. The paper demonstrates on fluidic topology and meta-surface tasks that this update lowers the target objective across all paired test samples.","pith_inferences":["Beyond the paper: the same evolution-strategy update could be applied in latent or score-based diffusion variants, provided the transition distribution is approximately Gaussian and samples can be drawn from it.","Beyond the paper: the method's apparent success on high-dimensional inputs suggests that the effective number of informative dimensions, not the pixel count, sets the sample complexity; this could be tested by perturbing only a subset of coordinates during guidance.","Beyond the paper: the weakest link is whether fitness at intermediate noising levels predicts fitness of the final design; a natural extension is to anneal $N_s$ or restrict guidance to late denoising steps where samples are close to valid designs."],"forward_implications":["Pre-trained diffusion models can be steered by any evaluator, including CFD solvers, electromagnetic simulators, or laboratory measurements, without training a differentiable surrogate or computing finite differences.","The number of solver calls per denoising step, $N_s$, and the scaling factor $\\alpha$ become direct controls over the trade-off between guidance strength and computational cost.","Because the update uses ranks rather than raw fitness values, the method is invariant to monotone rescaling of the objective, so users do not need to normalize different physics metrics before guiding generation.","The formal correspondence to gradient guidance means insights about $\\alpha$ scheduling and step-wise guidance transfer from classifier-guided diffusion to this derivative-free setting.","Guidance strength can be applied for only a fraction of the denoising steps; the paper shows meaningful objective improvement even with guidance restricted to the last ten of one hundred steps."],"supporting_citations":[{"why":"Defines the DDPM forward noising and reverse denoising Gaussian transitions that the proposed update modifies.","marker":"Ho et al. [2020]"},{"why":"Introduces classifier and regressor gradient guidance, the baseline update the paper's derivative-free update is shown to match.","marker":"Dhariwal and Nichol [2021]"},{"why":"Supplies the guided-denoising formulation as a gradient-based update to the Gaussian mean, which the paper contrasts with its own derivation.","marker":"Mazé and Ahmed [2023]"},{"why":"Provides natural evolution strategies, including the natural-gradient derivation and fitness shaping used in the algorithm.","marker":"Wierstra et al. [2014]"},{"why":"Provides the information-geometric optimization view of maximizing expected fitness under a population distribution.","marker":"Ollivier et al. [2017]"},{"why":"Supports the scalability claim that evolution strategies can perform well in high dimensions through low intrinsic dimensionality.","marker":"Salimans et al. [2017]"},{"why":"Contrast derivative-free guidance method built on the gradient rule; the paper claims its own update emerges from first principles.","marker":"Shen et al. [2025]"}],"fun_headline_variants":["Evolvable diffusion guides with black-box solvers, no derivatives","No-gradient diffusion guidance via evolutionary search","Diffusion guidance that works without any derivatives","Evolvable diffusion: black-box design without derivatives","Evolution meets diffusion for derivative-free guidance"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that evaluating the fitness function on partially denoised intermediate samples $x_t$ gives signal about the fitness of the final design $x_0$; if a solver or regressor trained only on final designs loses that signal as noise increases, the guidance update will not optimize the stated objective.","fun_headline_variants_meta":{"raw":{"variants":["Evolvable diffusion guides with black-box solvers, no derivatives","No-gradient diffusion guidance via evolutionary search","Diffusion guidance that works without any derivatives","Evolvable diffusion: black-box design without derivatives","Evolution meets diffusion for derivative-free guidance"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000414,"raw_usage":{"total_tokens":2132,"prompt_tokens":927,"completion_tokens":1205,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":543,"completion_tokens_details":{"reasoning_tokens":1134}},"tokens_in":543,"tokens_out":1205,"duration_ms":9193,"temperature":1.0,"reasoning_tokens":1134,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:05:48.460368+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On a task with a known fitness function, compute the correlation between $f(x_t)$ at the guidance steps used by the algorithm and $f(x_0)$ for samples from the unconditional model; if the correlation is near zero or negative while the method still reports improvement, the improvement must come from something other than the claimed evolutionary objective, and if the correlation is low the method should fail when guidance is restricted to early, high-noise steps.","supporting_citations":[{"cited_title":"Diffusion models beat GANs on topology optimization","cited_arxiv_id":null,"evidence_quote":"Supplies the guided-denoising formulation as a gradient-based update to the Gaussian mean, which the paper contrasts with its own derivation."},{"cited_title":"Natural evolution strategies","cited_arxiv_id":null,"evidence_quote":"Provides natural evolution strategies, including the natural-gradient derivation and fitness shaping used in the algorithm."},{"cited_title":"Information-geometric optimization algorithms: A unifying picture via invariance principles","cited_arxiv_id":null,"evidence_quote":"Provides the information-geometric optimization view of maximizing expected fitness under a population distribution."},{"cited_title":"Chemistry-inspired diffusion with non-differentiable guidance","cited_arxiv_id":null,"evidence_quote":"Contrast derivative-free guidance method built on the gradient rule; the paper claims its own update emerges from first principles."}],"review_version":1}