Advancements in optical coherence control1–5 have unlocked many cutting-edge applications, including long-haul communication, light detection and ranging (LiDAR) and optical coherence tomography6–8. Prevailing wisdom suggests that using more coherent light sources leads to enhanced system performance and device functionalities9–11. Our study introduces a photonic convolutional processing system that takes advantage of partially coherent light to boost computing parallelism without substantially sacrificing accuracy, potentially enabling larger-size photonic tensor cores. The reduction of the degree of coherence optimizes bandwidth use in the photonic convolutional processing system. This breakthrough challenges the traditional belief that coherence is essential or even advantageous in integrated photonic accelerators, thereby enabling the use of light sources with less rigorous feedback control and thermal-management requirements for high-throughput photonic computing. Here we demonstrate such a system in two photonic platforms for computing applications: a photonic tensor core using phase-change-material photonic memories that delivers parallel convolution operations to classify the gaits of ten patients with Parkinson’s disease with 92.2% accuracy (92.7% theoretically) and a silicon photonic tensor core with embedded electro-absorption modulators (EAMs) to facilitate 0.108 tera operations per second (TOPS) convolutional processing for classifying the Modified National Institute of Standards and Technology (MNIST) handwritten digits dataset with 92.4% accuracy (95.0% theoretically). Two photonic platforms using a convolutional processing system with partially coherent light sources is shown to boost computing parallelism, demonstrated using the classification of gaits of patients with Parkinson’s disease and the MNIST handwritten digits dataset.