TL;DR

Decision-time planning scores a candidate only by how close its predicted final state is to the goal, never checking that the route there is realizable. ACID adds cycle action consistency: an inverse dynamics model infers the action behind each predicted transition, and its mismatch with the conditioning action becomes a per-step planning cost — improving planning across four world models and six tasks with substantially less compute.

Overall architecture of ACID

(Left): Decision-time planning with an action-conditioned world model: an MPC with CEM searches over candidate action sequences $a_{0:H-1}a\_\{0:H-1\}$ to minimize the augmented planning cost. The current observation $o_{0}o\_0$ is encoded by $E_{\theta }E\_\backslash theta$ to $z_{0}z\_0$, and the world model $F_{\theta }F\_\backslash theta$ unrolls a latent trajectory ${\widehat{z}}_{1:H}\backslash hat\{z\}\_\{1:H\}$ from $(z_0,a_{0:H-1})(z\_0,\; a\_\{0:H-1\})$. The inverse dynamics model $G_{\varphi }G\_\backslash phi$ then takes each predicted transition $({\widehat{z}}_t,{\widehat{z}}_{t+1})(\backslash hat\{z\}\_t,\; \backslash hat\{z\}\_\{t+1\})$ and infers the action ${\widehat{a}}_t\backslash hat\{a\}\_t$ that would explain it.
(Right): The augmented planning cost combines two terms: the goal cost, which prefers candidate action sequences whose predicted final latent is close to the goal, and the action consistency cost, which prefers candidate action sequences whose predicted trajectory is realizable in environment.