Despite strong results on recognition and segmentation, current 3D visual pre-training methods often underperform on robotic manipulation. We attribute this gap to two factors: the lack of state-action-state dynamics modeling and the unnecessary redundancy of explicit geometric reconstruction. We introduce AFRO, a self-supervised framework that learns dynamics-aware 3D representations without action or reconstruction supervision. AFRO casts state prediction as a generative diffusion process and jointly models forward and inverse dynamics in a shared latent space to capture causal transition structure. To prevent feature leakage in action learning, we employ feature differencing and inverse-consistency supervision, improving the quality and stability of visual features. When combined with Diffusion Policy, AFRO substantially increases manipulation success rates across 16 simulated and 4 real-world tasks, outperforming existing pre-training approaches. The framework also scales favorably with data volume and task complexity. Qualitative visualizations indicate that AFRO learns semantically rich, discriminative features, offering an effective pre-training solution for 3D representation learning in robotics. Project page: https://kolakivy.github.io/AFRO/

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