Paper Summary
Paperzilla title
Flow Maps Learn from Themselves: Lagrangian Method Shows Off Its Stability!
This paper presents a unified algorithmic framework for training consistency models, which accelerate generative modeling by learning flow maps via self-distillation. The authors introduce three algorithmic families (Eulerian, Lagrangian, Progressive), demonstrating that the novel Lagrangian method offers significantly more stable training and higher performance compared to existing schemes, though some methods still struggle with fine details or higher step counts.
Possible Conflicts of Interest
None identified
Identified Weaknesses
Eulerian Scheme Instability
The Eulerian distillation (ESD) method was found to be unstable during training and showed poor performance, particularly on datasets like CelebA-64, where results were not reported. This limits its practical applicability.
Struggles with Sharp Features
On datasets with very sharp features (e.g., Checkerboard), all methods, including the new Lagrangian and Progressive variants, exhibited some difficulty in capturing these sharp boundaries accurately or introduced artifacts at small step counts.
Lagrangian Method Performance at High Step Counts
While generally superior, the Lagrangian Self-Distillation (LSD) method performs less effectively than other variants (like PSD-M) at higher step counts (e.g., N=16 for CIFAR-10), indicating a trade-off in performance characteristics.
Rating Explanation
This paper provides a significant contribution by presenting a unified framework for consistency models and introducing novel Lagrangian methods for learning flow maps. The theoretical foundation is solid, and empirical results demonstrate improved stability and performance, particularly with the Lagrangian approach. While some limitations exist regarding performance on sharp features and specific step counts for different methods, the overall work advances the field of accelerated generative modeling.
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File Information
Original Title:
How to build a consistency model: Learning flow maps via self-distillation
Uploaded:
October 07, 2025 at 07:31 PM
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