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Machine learning based methods have shown potential for optimizing existing molecules with more desirable properties, a critical step towards accelerating new chemical discovery. Here we propose QMO, a generic query-based molecule optimization framework that exploits latent embeddings from a molecule autoencoder. QMO improves the desired properties of an input molecule based on efficient queries, guided by a set of molecular property predictions and evaluation metrics. We show that QMO outperforms existing methods in the benchmark tasks of optimizing small organic molecules for drug-likeness and solubility under similarity constraints. We also demonstrate significant property improvement using QMO on two new and challenging tasks that are also important in real-world discovery problems: (i) optimizing existing potential SARS-CoV-2 Main Protease inhibitors toward higher binding affinity; and (ii) improving known antimicrobial peptides towards lower toxicity. Results from QMO show high consistency with external validations, suggesting effective means to facilitate material optimization problems with design constraints.