Traditional screening-based drug discovery is inherently limited by the astronomical scale of the underlying chemical space. Generative modelling offers a compelling alternative to the classical search paradigm and enables rational, bottom-up design of novel and target-specific small molecules. However, its impact has been hampered by challenges in synthetic accessibility of the designed compounds and lack of large-scale experimental validation. Here, we introduce LDDM (Large Drug Discovery Model), a generative framework that supports a wide range of drug discovery tasks, including constrained and unconstrained docking, fragment linking and growing, and de novo design. We further introduce a programmable design algorithm that enables accurate and synthesizable design of compounds satisfying various fine-grained objectives. We experimentally validated optimized and de novo designed peptide and small-molecule binders for seven therapeutically relevant proteins: CDO1, cathepsin S, Pin1, PGK1, KRAS, BRD4, and SARS-CoV-2 Nsp3. The best designs were structurally characterized through competition experiments, NMR spectroscopy, and X-ray crystallography, demonstrating high 3D modelling accuracy. Overall, LDDM provides a scalable and flexible platform for the rapid and tailored design of small molecules and non-natural peptides for diagnostic and therapeutic applications.