Foundations of Diffusion Models in General State Spaces: A Self-Contained Introduction

arXiv — stat.MLFriday, December 5, 2025 at 5:00:00 AM
  • A new article on arXiv presents a self-contained introduction to diffusion models in general state spaces, bridging the gap between continuous and discrete data structures. It discusses the development of discrete-time views through Markov kernels and reverse dynamics, as well as continuous-time limits involving stochastic differential equations and continuous-time Markov chains, culminating in the derivation of Fokker–Planck and master equations.
  • This development is significant as it enhances the understanding of diffusion models, which are increasingly central to generative modeling. By unifying various state spaces, the article provides a comprehensive framework that could facilitate advancements in machine learning applications, particularly in generative tasks where data may not fit traditional Euclidean assumptions.
  • The exploration of diffusion models reflects a broader trend in artificial intelligence towards integrating diverse methodologies, such as reinforcement learning and maximum entropy frameworks. This convergence aims to improve the efficiency and effectiveness of generative models, addressing challenges like reward alignment and data generation control, which are critical for the future of AI-driven technologies.
— via World Pulse Now AI Editorial System

Was this article worth reading? Share it

Recommended apps based on your readingExplore all apps
Continue Readings
Convergence of Stochastic Gradient Langevin Dynamics in the Lazy Training Regime
NeutralArtificial Intelligence
A recent study published on arXiv presents a non-asymptotic convergence analysis of stochastic gradient Langevin dynamics (SGLD) in the lazy training regime, demonstrating that SGLD achieves exponential convergence to the empirical risk minimizer under certain conditions. The findings are supported by numerical examples in regression settings.
LongVT: Incentivizing "Thinking with Long Videos" via Native Tool Calling
PositiveArtificial Intelligence
LongVT has been introduced as an innovative framework designed to enhance video reasoning capabilities in large multimodal models (LMMs) by facilitating a process known as 'Thinking with Long Videos.' This approach utilizes a global-to-local reasoning loop, allowing models to focus on specific video clips and retrieve relevant visual evidence, thereby addressing challenges associated with long-form video processing.
LangSAT: A Novel Framework Combining NLP and Reinforcement Learning for SAT Solving
PositiveArtificial Intelligence
A novel framework named LangSAT has been introduced, which integrates reinforcement learning (RL) with natural language processing (NLP) to enhance Boolean satisfiability (SAT) solving. This system allows users to input standard English descriptions, which are then converted into Conjunctive Normal Form (CNF) expressions for solving, thus improving accessibility and efficiency in SAT-solving processes.
Geschlechts\"ubergreifende Maskulina im Sprachgebrauch Eine korpusbasierte Untersuchung zu lexemspezifischen Unterschieden
NeutralArtificial Intelligence
A recent study published on arXiv investigates the use of generic masculines (GM) in contemporary German press texts, analyzing their distribution and linguistic characteristics. The research focuses on lexeme-specific differences among personal nouns, revealing significant variations, particularly between passive role nouns and prestige-related personal nouns, based on a corpus of 6,195 annotated tokens.
Limit cycles for speech
PositiveArtificial Intelligence
Recent research has uncovered a limit cycle organization in the articulatory movements that generate human speech, challenging the conventional view of speech as discrete actions. This study reveals that rhythmicity, often associated with acoustic energy and neuronal excitations, is also present in the motor activities involved in speech production.
Control Illusion: The Failure of Instruction Hierarchies in Large Language Models
NegativeArtificial Intelligence
Recent research highlights the limitations of hierarchical instruction schemes in large language models (LLMs), revealing that these models struggle with consistent instruction prioritization, even in simple cases. The study introduces a systematic evaluation framework to assess how effectively LLMs enforce these hierarchies, finding that the common separation of system and user prompts fails to create a reliable structure.
CARL: Critical Action Focused Reinforcement Learning for Multi-Step Agent
PositiveArtificial Intelligence
CARL, a new reinforcement learning algorithm, has been introduced to enhance the performance of multi-step agents by focusing on critical actions rather than treating all actions equally. This approach addresses the limitations of conventional policy optimization methods, which often overlook the varying importance of different actions in achieving desired outcomes.
FusionBench: A Unified Library and Comprehensive Benchmark for Deep Model Fusion
PositiveArtificial Intelligence
FusionBench has been introduced as a unified library and benchmark specifically designed for deep model fusion, allowing for the evaluation and comparison of various fusion methods across multiple tasks and datasets. This initiative aims to address the inconsistencies in the evaluation of deep model fusion techniques, enhancing their effectiveness and robustness.