Though new affordable high power laser technologies make possible many processing applications in science and industry, depth control remains a serious technical challenge. Here we show that inline coherent imaging, with line rates up to 312 kHz and microsecond-duration capture times, is capable of directly measuring laser penetration depth in a process as violent as kW-class keyhole welding. We exploit ICIs high speed, high dynamic range and robustness to interference from other optical sources to achieve fully automatic, adaptive control of laser welding as well as ablation, achieving micron-scale sculpting in vastly different heterogeneous biological materials.