This paper reviews how machine learning is shifting materials discovery from predicting properties to proposing candidate materials that meet specific goals and physical limits. The authors focus on crystalline solids and bring together three areas: generative models that can create crystal structures, multimodal learning that combines many types of materials data, and closed-loop workflows that propose, test, and refine candidates automatically.

The review surveys leading classes of generative models and explains how they work at a high level. It covers variational autoencoders (VAE), normalizing flows, autoregressive models, and diffusion models. These generators learn chemical and structural “priors” from large databases so they can sample plausible periodic structures. The authors also describe practical ways to enforce feasibility. That includes choices of how to represent structures, training objectives, guiding samples at generation time, and post-generation screening and relaxation steps.

The paper stresses that materials knowledge is multimodal. Useful signals come not only from crystal coordinates but also from thermodynamic and electronic data, microscopy images, spectra, processing logs, and scientific text. Multimodal learning aims to fuse these signals into representations that are more transferable and more useful for conditioning a design search. The review also examines inverse-design strategies that combine conditional generation with techniques such as latent-space optimization, Bayesian optimization, reinforcement learning, and active learning.

The authors describe a closed-loop framework made of three iterative steps: proposal, evaluation, and feedback. Proposal means generating candidates with a generator or search method. Evaluation moves from cheap validity checks and surrogate predictors up to high-fidelity validation such as density functional theory (DFT) relaxations or targeted experiments. Feedback updates the proposal mechanism so later iterations focus on more promising regions while keeping diversity and correct uncertainty estimates. Mathematically, inverse design is framed as finding materials x that maximize a utility U(x) while remaining inside the feasible set defined by physical and practical constraints.