The Art and Science of Diffusion models Expertly crafted for graduate students in physics and computer science, offering a semester-long, thorough exploration of Denoising Diffusion Probabilistic Models (DDPMs) within the expansive field of generative AI. Unlike conventional texts that follow a rigid definition-theorem-proof format, this book adopts a more relaxed and conversational tone, incorporating extensive commentary, motivation, and explanations to enhance understanding and engagement. Rich with a vast array of fully solved examples and exercises of varying complexity, this manuscript integrates these into the narrative to enhance and assess the reader's understanding extensively. These exercises are central to the book's structure, often referenced in subsequent discussions to encourage a dynamic and interactive learning environment. In the field of AI, Shlomo demonstrated his leadership by guiding research teams to innovative breakthroughs and has written comprehensive publically available book on Deep Learning. Amazon GitHub About the Book Until recently, diffusion models were a niche known only to a select group of scientists and engineers. Generative AI, a field heavily reliant on these models, requires an intricate understanding of mathematics, physics, stochastic processes, deep learning, and computer science. This volume stands out by concentrating solely on diffusion models, offering a unique perspective rarely found in other texts. This focused approach not only simplifies complex ideas for a broader audience but also pushes the boundaries of what AI can achieve in modern industries and research. As such, this book is an essential resource for anyone seeking to understand the current and future impacts of technology-driven creative processes in Generative AI. The book offers a detailed exploration of key concepts including Brownian motion, Itô's lemma, Stochastic Differential Equations (SDEs), and the significant role of stochastic processes in artificial intelligence. It provides an exhaustive introduction to diffusion processes, a meticulous examination of DDPMs, and a chapter dedicated to the deep learning architectures fundamental to DDPMs. The narrative is enriched with a plethora of solved problems and numerous programming mini-projects, concentrating mainly on results that hold substantial relevance for practical implementations. As an extensive graduate-level textbook and reference, it embraces the philosophy that the most effective way to learn about DDPM's is through its application, illustrated through extensive examples that demonstrate the theory in real-world scenarios. Table of Contents About the Author Shlomo Kashani Shlomo's commitment to lifelong learning is clearly illustrated by his pursuit of three academic degrees with a fourth on the horizon—a testament to his unwavering thirst for knowledge. Shlomo's academic focus on AI and Quantum Computing has been nothing short of inspirational, reflecting his passion for innovation, adaptability in the face of new challenges, and continuous intellectual expansion. His current postgraduate studies in Diplomacy at SOAS in London are complemented by previous explorations into Quantum Physics at the esteemed Johns Hopkins University (JHU) and Digital Signal Processing at Queen Mary University Of London (QMUL), all of which underscore his relentless quest to broaden his intellectual knowledge base.