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The inverse design of materials with desired target properties remains one of the central challenges in computational materials science. Despite recent advances in generative modeling applied to materials, most diffusion-based methods are limited to unconditional sampling or require retraining on large, property-labeled datasets to enable property conditioning. In addition to high computational costs associated with retraining and fine-tuning, this restricts their applicability to new design objectives or compositional constraints that lack sufficient data. To address this limitation, we introduce a hybrid diffusion-genetic algorithm framework that enables on-the-fly optimization of target material properties during the generative process, without retraining or requiring differentiable property predictors. Our framework couples the generative power of pre-trained diffusion models with the adaptive optimization and search capabilities of genetic algorithms. At intermediate stages of the diffusion denoising trajectory (termed the horizon), it evaluates partially denoised crystal candidates by fully denoising them and assigns them a score using black-box scoring functions such as machine-learned surrogates or physics-based property calculators. This score is then used to update the latent vectors at the horizon to guide subsequent generations through selection, crossover, and mutation in latent space. This creates a closed-loop optimization scheme that adaptively refines the reversed-diffusion trajectory toward high-performing, stable, and novel materials. This approach is fully model-agnostic and can integrate with a wide range of generative models such as diffusion, flow matching, and stochastic interpolants frameworks without modification of the underlying model or loss function. We demonstrate the utility of our framework using MatterGen, a state-of-the-art generative model for periodic crystal structures. Specifically, we target the generation of Ti-Al-N crystal structures with a specified shear modulus of 160 GPa, the discovery of low-energy Li-X-Y halide materials under compositional constraints (e.g., Li + halide + non-oxide species), and the design of perovskites in the Cs-Sn-I chemical space with a prescribed energy above the convex hull. Across a large hyperparameter space, we achieve substantial improvements in property optimization compared to diffusion-only or GA-only baselines. The quality of generated materials is evaluated using the Stability, Uniqueness, and Novelty (SUN) metrics introduced in MatterGen, showing that the framework maintains structural diversity and novelty while achieving higher target property scores than those observed in MatterGen-only sampling. In fact, for 'hit-finding' tasks, the method only needs a single generation of optimization to generate a structure matching any required constraint. None of the above examples could be achieved with MatterGen alone without extensive retraining or property-specific datasets, and for cases where MatterGen can generate valid structures with constraints - such as the energy above the hull - our method produces a larger number of candidates that satisfy the user-defined compositional and property constraints. We demonstrate that our novel hybrid diffusion-genetic algorithm framework effectively bridges generative modeling and optimization in materials discovery - achieving controllable, property-guided generation from pre-trained diffusion models without labeled datasets or fine-tuning. It provides a general and extensible framework for guided crystal generation under compositional and property constraints, offering a pathway toward automated exploration of vast chemical spaces with user-defined objectives. Ongoing work extends this framework to multi-objective optimization (like stability-elasticity trade-offs) and large-scale benchmarking across compositional families, paving the way for its integration into high-throughput materials discovery workflows.
