Casacuberta, CarlesEscalera Guerrero, SergioPujol Vidal, Àlex2025-01-232025-01-232024-09-02https://hdl.handle.net/2445/217853Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Carles Casacuberta i Sergio Escalera GuerreroIn this thesis we explore the fundamental principles of Binary Latent Diffusion Models (BLDM), a novel class of generative models that leverage probabilistic deep latent variable models and diffusion processes to approximate complex data distributions. The research delves into probability theory, generative models, and latent space representations, with a focus on Variational Autoencoders (VAE) that lead to Bernoulli Variational Autoencoders (BVAE). The study provides a comprehensive overview of the foundations of Diffusion Models, leading to the formal definition of Discrete Bernoulli Diffusion Models (DBDM) and its training objective. Both, BVAE and DBDM, are the building blocks of the BLDM. Additionally, a practical application is presented. This exploration highlights the mathematical formalization and implementation strategies for BLDMs, paving the way for future advancements in generative modeling.82 p.application/pdfengcc by-nc-nd (c) Àlex Pujol Vidal, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/Aprenentatge automàticProbabilitats combinatòriesTreballs de fi de màsterMachine learningCombinatorial probabilitiesMaster's thesisinfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccess