Rethinking Causal Action Tokenization with Conditional Annealing in Flow Matching

CATok grounds discrete action tokens in the continuous flow-matching trajectory — a causally ordered, coarse-to-fine action representation for autoregressive VLA models.

Chenyu Zhang^1,2*, Yuhang Cao^1*, Daru Du^1,2, Yingxi Lu^1,2, Jing Shao¹, Ruoqu Chen^1,2, Jiajun Liu^1,2, Liu Cao^1,2, Yicheng Liu¹, Hang Zhao^1,2, Mengdi Xu^1,2†

¹IIIS, Tsinghua University ²Shanghai Qizhi Institute

^*Equal Contribution ^†Corresponding Author

**Flow-Matching to Action Tokens.** Each discrete token encodes the residual reconstruction signal at a specific flow-matching stage, establishing a coarse-to-fine causal token space aligned with autoregressive modeling.