DiffGA: Steering Frozen Diffusion Models for Materials Design via Evolutionary Search

Shivang Agarwal; Rodrigo Wang; Kevin Ryczko; Aayush R. Singh

cond-mat.mtrl-sciOct 10, 2026

DiffGA: Steering Frozen Diffusion Models for Materials Design via Evolutionary Search

Authors: Shivang Agarwal, Rodrigo Wang, Kevin Ryczko, Aayush R. Singh

Organizations: SandboxAQ, Palo Alto, CA 94301, USA.

Abstract

Steering candidate generation toward user-defined objectives is central to inverse materials design, yet remains difficult when objectives are black-box, changing, or non-differentiable, as in many simulation- and experiment-derived properties. Generative models offer a solution but typically require retraining or fine-tuning for each new objective, demanding labeled data and substantial compute, or rely on differentiable guidance that is brittle to gradient noise and undefined for many practical targets. We present DiffGA, a retraining-free framework that injects evolutionary search into the sampling trajectory of a retrained diffusion model, evolving partially denoised states under an arbitrary black-box oracle. Because oracle evaluation often dominates campaign cost, we couple DiffGA with an on-the-fly Bayesian surrogate that reuses representations from state-of-the-art machine-learned force fields (MLFFs). A Gaussian process is fit during the campaign on the force fields's graph embeddings and, once it demonstrably ranks an unseen generation, replaces expensive property evaluations under an uncertainty-aware acquisition rule, reducing oracle cost with negligible loss of accuracy. Across three crystal-design tasks using a frozen MatterGen backbone, DiffGA outperforms diffusion-only, compute-matched, purely evolutionary, and fine-tuned baselines in oracle-assessed rates of stable, unique, and novel hits. Rather than proposing scientific compounds, we use density functional theory to quantify MLFF oracle fidelity, showing that it is a faithful proxy in key regimes but systematically biased in others, delineating when proxy-driven generative discovery can be trusted. On a representative sample, DiffGA's top hits survive first principles re-evaluation as physically realistic hits, while the surrogate-accelerated pipeline preserves this fidelity at a fraction of the cost.

Figures & tables

Figure 1: A schematic overview of the DiffGA workflow for diffusion models and the experiments performed in this study. Details about each step can be found in the Methods section.

Exp.	Method	Mean HR (%)	Mean SUN HR (%)	Best SUN HR (%)
A	Diff. $\dagger$	14.51 b	1.38 b	4.17 b
	Diff. $\ddagger$	82.98 b	8.18 b	15.78 b
	GA	77.78 b	8.58 b	19.22 b
	DiffGA	83.26 b	9.55 b	19.22 b
B	Diff. $\dagger$	2.08 c / 1.46 b / 0.07 a	0.58 c / 0.19 b / 0.02 a	2.08 c / 0.69 b / 0.35 a
	Diff. $\ddagger$	3.47 c / 1.74 b / 0.11 a	1.73 c / 0.69 b / 0.08 a	9.37 c / 6.25 b /0.42 a

Table 1: Hit rate (HR) metrics for each experiment. We compare diffusion (first-generation

\dagger

and compute-matched baselines

\ddagger

), GA, and DiffGA, and evaluate performance across three pretrained MatterGen variants: mattergen_base a , chemical_system b , and chemical_system_energy_above_hull c .

Panel of Figure 2 — Figure 2: The average number of hits across generations for experiment B for each value of $P$ , averaged across the three seeds. The models used are: (a, b, c) chemical_system_energy_above_hull , (d, e, f) chemical_system , and (g, h, i) mattergen_base . For clarity, the legend has only been shown in the first plot but applies to all figures, and for (g, h, i), we plot every $2^{\text{nd}}$ data point.

Figure 3: Joint UMAP of pooled GemNet node embeddings evaluated at the final denoising step for unconditional mattergen_base samples, reference transition metal carbides, and DiffGA populations at generations 4 and 15 for experiment C. Contours enclose 50% and 90% of each set’s density. The black stars mark the four DFT‑validated high‑shear‑modulus hits (Table 2 ).

Panel of Figure 4 — Figure 4: Pareto frontier plots for experiment B using different models: (a) chemical_system_energy_above_hull , (b) chemical_system , and (c) mattergen_base .

Panel of Figure 5 — Figure 5: (a, b, c) Optimization performance preservation and (d, e, f) oracle efficiency improvement for different horizon times, $t_{h}$ , averaged over three seeds. For (a, b, c), the ratio shown is the number of SUN hits for the surrogate-accelerated (SA) pipeline to those for the traditional (T) DiffGA pipeline. For (d, e, f), the ratio is reversed. Experiment A used the chemical_system model, whereas experiments B and C use the mattergen_base model. For clarity, the y axes labels and legends have only been shown on the first column but hold true for all plots. For experiment C, error bars have been omitted due to large variations (courtesy of extremely low hit rates). Overall, the surrogate-accelerated pipeline maintains comparable performance while drastically increasing efficiency.

Panel of Figure 6 — Figure 6: Oracle fidelity across experiments by comparing against DFT baselines. (a) Relaxed-ion shear moduli (GPa) and (b) clamped-ion shear moduli (GPa) correlation for Ti-Al-N and transition metal carbide systems, and (c) energy above the hull (eV/atom) correlation for Cs-Sn-I systems.

SUN	MatTen	DFT	DFT	Highest MP	Normalized	Energy above the
Hit	(GPa)	Clamped-ion (GPa)	Relaxed-ion (GPa)	value (GPa)	RMSD	hull (eV/atom)
WC	$261.18$	$295.26$	$289.58$	$263.151$	$1.6\times 10^{-3}$	$0.0164$
CrC	$228.06$	$263.73$	$254.15$	$249.439$	$3.6\times 10^{-3}$	$0.1023$
CrC	$236.41$	$252.33$	$243.01$	$249.439$	$1.9\times 10^{-3}$	$0.1255$
CrC	$221.70$	$251.18$	$242.57$	$249.439$	$1.6\times 10^{-4}$	$0.1144$

Table 2: DFT validation of the top transition metal carbide SUN hits showing MatTen- and DFT-computed shear moduli (in GPa), normalized RMSD between the MLFF‑relaxed and DFT‑relaxed structures, and DFT (r2SCAN) energy above hull (eV/atom). The highest shear moduli (G) for a given chemical space reported in the MP database is also presented.

Figure 7: Visual representation of how a single structure is obtained via evolutionary operations and subsequent denoising. Here, $t_{h}=0.5$ . Note that ‘Parent A’, ‘Parent B’, ‘Child’, and ‘Mutated Child’ all exist at $t=t_{h}$ . The Md atoms are noisy placeholders introduced by the underlying diffusion model for atom types yet to be fully denoised.

Panel of Figure 8 — Figure 8: Spearman rank correlation between surrogate-predicted and true oracle properties evaluated on the most recent generation, for all experiments and $t_{h}$ values. Rank correlations remain high throughout the campaigns, demonstrating that the surrogate preserves the candidate ranking required by the evolutionary selection step. Markers show the mean across all seeds and error bars denote the standard deviation across seeds.

Panel of Figure 9 — Figure 9: The average number of hits across generations for (a, b, c) experiment A and (d, e, f) experiment C for each value of $P$ , averaged across the three seeds. For clarity, the legend has only been shown in the first plot but applies to all figures, and for (d, e, f), we plot every $2^{\text{nd}}$ data point.

Panel of Figure 10 — Figure 10: Pareto frontier-based trade-off analysis for (a) experiment A and (b) experiment C.

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