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Learn to build consistency models through a comprehensive technical presentation that introduces a systematic algorithmic framework for directly learning flow maps associated with flow or diffusion models. Explore how to convert distillation schemes into direct training algorithms via self-distillation, eliminating the need for pre-trained teachers by exploiting the relationship between velocity fields and instantaneous rate changes in flow maps. Discover three distinct algorithmic families - Eulerian, Lagrangian, and Progressive methods - that encompass and extend all known distillation and direct training schemes for consistency models. Examine how Lagrangian methods achieve superior stability and performance by avoiding spatial derivatives and bootstrapping from small steps, while understanding the unified framework that reveals new design principles for accelerated generative modeling in AI-driven drug discovery applications.