Beyond Implicit Mapping: Advancing Generative Models Through Smoothed Optimal Transport

Area of Science:

• Deep learning
• Generative models
• Optimal transport theory

Background:

• Optimal transport (OT) is crucial in deep learning for distribution transformation.
• Current OT methods in deep generative models often use implicit mappings, limiting interpretability and conditional generation.
• Existing models face challenges like training instability, vanishing gradients, and mode collapse.

Purpose of the Study:

• To develop an advanced generative model with an explicit optimal transport mapping.
• To enhance model interpretability and enable effective conditional sample generation.
• To improve the efficiency of sample generation in deep learning models.

Main Methods:

• Applied Nesterov's smoothing technique to the Brenier potential.
• Derived an explicit optimal transport mapping from the smoothed potential.
• Constructed a novel deep generative model based on this explicit mapping.

Main Results:

• The proposed model explicitly captures source-to-target domain mappings, improving interpretability.
• Enabled conditional sample generation via a smoothed OT mapping approximation.
• Achieved superior performance in both unconditional and conditional generation tasks compared to traditional methods.

Conclusions:

• The novel approach provides an interpretable and efficient generative model.
• Explicit OT mappings derived through smoothing offer a new direction for generative modeling.
• The method successfully addresses limitations of implicit OT mappings in deep learning.