Tensor-Valued Time and Inference Path Optimization in Differential Equation-Based Generative Modeling

2024-04-22

AI Summary

Existing flow- and diffusion-based generative models exhibit training stability but are constrained by scalar-valued time modeling, lacking dimensional flexibility and adaptability to diverse inference trajectories. This work introduces tensor-valued time—replacing scalar time—to enable dimensionally scalable temporal representations. We further propose a solver-guided adaptive multidimensional inference path optimization method that jointly improves generation quality and sampling efficiency under a fixed number of function evaluations. Our core contributions are threefold: (1) the first tensor-time modeling framework for generative differential equations; (2) a novel paradigm for adaptive multidimensional path optimization in ODE/SDE-based generative modeling; and (3) mechanistic insights into how temporal dimension expansion enhances both training dynamics and inference performance. Experiments demonstrate that tensor time alone yields substantial inference improvements, and integrating path optimization consistently boosts performance across benchmarks.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

In the field of generative modeling based on differential equations, conventional methods utilize scalar-valued time during both the training and inference phases. This work introduces, for the first time, a tensor-valued time that expands the conventional scalar-valued time into multiple dimensions. Additionally, we propose a novel path optimization problem designed to adaptively determine multidimensional inference trajectories using a predetermined differential equation solver and a fixed number of function evaluations. Our approach leverages the stochastic interpolant framework, simulation dynamics, and adversarial training to optimize the inference pathway. Notably, incorporating tensor-valued time during training improves some models' inference performance, even without path optimization. When the adaptive, multidimensional path derived from our optimization process is employed, further performance gains are achieved despite the fixed solver configurations. The introduction of tensor-valued time not only enhances the efficiency of models but also opens new avenues for exploration in training and inference methodologies, highlighting the potential of adaptive multidimensional paths.

Problem

• Extends flow and diffusion models to multidimensional coefficients
• Enables adaptive inference trajectory optimization
• Improves generative quality with training efficiency

Innovation

• Multidimensional Adaptive Coefficient for trajectory optimization
• Adversarial refinement for simulation-based feedback
• Plug-in module enhancing flow and diffusion models