Manifold-Aligned Generative Transport

arXiv:2602.19600 · stat.ML, cs.LG · Submitted 2026-02-23 · Read on arXiv

stat.ML, cs.LG

Submitted: 2026-02-23

Updated: 2026-09-08

Comments: 70 pages, including supplementary materials

Code: https://github.com/huggingface/diffusers

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Fidelity — 35× in this paper · explained in 2 episodes
• Flow Matching — 19× in this paper · explained in 7 episodes
• Benchmark — 18× in this paper · explained in 2 episodes
• Diffusion Model — 15× in this paper · explained in 8 episodes
• Diffusion Models — 15× in this paper · explained in 6 episodes
• Normalizing Flow — 10× in this paper · explained in 3 episodes
• Normalizing Flows — 10× in this paper · explained in 4 episodes
• Alignment — 9× in this paper · explained in 1 episode
• Intrinsic Dimension — 9× in this paper · explained in 2 episodes
• Generative Modeling — 8× in this paper · explained in 3 episodes
• Accuracy — 6× in this paper · explained in 1 episode
• Manifold-Aligned Generative Transport — 6× in this paper
• Ambient Dimension — 4× in this paper · explained in 1 episode
• Distillation — 4× in this paper · explained in 2 episodes
• Generative Model — 4× in this paper · explained in 2 episodes
• Generative Models — 4× in this paper · explained in 2 episodes
• Embeddings — 3× in this paper · explained in 2 episodes
• International Conference on Learning Representations — 3× in this paper
• Anchor Loss — 2× in this paper · explained in 1 episode
• Latent Space — 2× in this paper · explained in 7 episodes
• Minimax optimality — 2× in this paper · explained in 2 episodes
• Optimal Transport — 2× in this paper · explained in 5 episodes
• Rectified Flow — 2× in this paper · explained in 3 episodes
• Wasserstein Distance — 2× in this paper · explained in 4 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Adaptivity — 1× in this paper · explained in 1 episode
• Approximation Bound — 1× in this paper · explained in 1 episode
• Computational Biology — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Diffusion Process — 1× in this paper · explained in 2 episodes
• Fisher Information — 1× in this paper · explained in 3 episodes
• Iterative Refinement — 1× in this paper · explained in 3 episodes
• Latent Diffusion Model — 1× in this paper · explained in 2 episodes
• Latent Diffusion Models — 1× in this paper · explained in 2 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes
• Society for Industrial and Applied Mathematics — 1× in this paper
• Sparsity — 1× in this paper · explained in 4 episodes
• Stochastic Gradient Descent (SGD) — 1× in this paper · explained in 5 episodes
• Synthetic Data Generation — 1× in this paper · explained in 5 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes

Sources

• On the minimax optimality of Flow Matching through the connection to kernel density estimation
• Flow Matching for Generative Modeling
• Rectified Flow: A Marginal Preserving Approach to Optimal Transport
• Denoising Diffusion Implicit Models

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