Real-time chunking (RTC) lets chunked action policies operate under inference delay by conditioning a newly generated action chunk on actions already committed by the previous chunk. Training-time RTC simulates this delay during learning and avoids expensive guidance at deployment, but its binary prefix mask treats all non-prefix tokens as fully unconstrained. This under-models asynchronous execution: early overlap actions are fixed, while later overlap actions remain editable but should still stay close to the previous plan. We propose Soft RTC, a training-time RTC generalization based on action-prior denoising. Soft RTC constructs corrupted overlap tokens from partially denoised states instead of pure noise and injects the aligned previous chunk as the same prior during inference through a lightweight token-wise blending rule. On the 12 released large Kinetix levels, a short soft window nearly matches hard training-time RTC in overall solve rate (0.809 vs. 0.815), while a medium window reduces high-delay action delta and jerk by 9.1% and 9.6% relative to hard RTC. Both variants keep near-naive runtime, unlike inference-time RTC baselines. A small preliminary real-robot sorting study provides additional evidence that training-time RTC can improve completion and that Soft RTC gives the lowest commanded-action finite-difference metrics among the tested policies.