Focused transmits are the most commonly used transmit strategy for echocardiograms, but suffer from relatively low frame rates, and in 3D, even lower volume rates. Fast imaging based on unfocused transmits has disadvantages such as motion decorrelation and limited harmonic imaging capabilities. This work introduces a patient-adaptive focused transmit and receive scheme that has the ability to drastically reduce the number of transmits needed to produce a high-quality ultrasound image. The method relies on posterior sampling with a temporal diffusion model to perceive and reconstruct the anatomy based on partial observations, while subsequently acquiring the most informative transmits. This cognitive ultrasound modality outperforms random and equispaced subsampling in terms of distortion and perceptual metrics on the 2D EchoNet-Dynamic dataset and a 3D Philips dataset, where we actively select focused elevation planes. Furthermore, our method improves generalized contrast-to-noise ratio from 0.83 to 0.89 compared to the same number of diverging wave transmits on six in-house echocardiograms. Additionally, we can segment the left ventricle, with on average 0.91 Dice-Sørensen coefficient, through simulating using 2 out of 112 lines. Finally, our method can be run in real-time on GPU accelerators from 2023, increasing the maximum achievable frame-rate from 46 Hz to 58 Hz. The code is publicly available at https://tue-bmd.github.io/casl/.