Convergence Guarantees for Time-Inhomogeneous Uniform-Rate Discrete Diffusion Models.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Generative Models

Background:

• Discrete diffusion models are powerful for categorical data generation.
• Theoretical understanding is limited, especially for time-inhomogeneous noise schedules.
• Current models often rely on time-homogeneous Markov chains.

Purpose of the Study:

• To theoretically analyze discrete diffusion models with time-inhomogeneous continuous-time Markov chain forward processes.
• To establish convergence guarantees for reverse-time samplers in these models.
• To provide a framework for understanding sampling error decomposition.

Main Methods:

• Studying uniform-rate discrete diffusion models with continuous-time Markov chain forward processes.
• Directly controlling total variation distance to establish convergence guarantees.
• Decomposing sampling error into initialization, score-estimation, discretization, and early-stopping components.

Main Results:

• Established convergence guarantees for practical reverse-time samplers.
• Provided explicit characterization of sampling error terms based on noise accumulation, local rate, and schedule smoothness.
• Derived step-complexity guarantees matching existing results for homogeneous samplers under regularity conditions.

Conclusions:

• The study offers a robust theoretical understanding of discrete diffusion models with time-inhomogeneous noise schedules.
• The direct control of total variation distance provides a more effective route to analyzing sampler convergence.
• The findings pave the way for more efficient and reliable generative models for categorical data.