Recent literature suggests that tri-exponential models may provide additional information and fit liver intravoxel incoherent motion (IVIM) data more accurately than conventional bi-exponential models. However, voxel-wise fitting of IVIM results in noisy and unreliable parameter maps. For bi-exponential IVIM, neural networks (NN) were able to produce superior parameter maps than conventional least-squares (LSQ) generated images. Hence, to improve parameter map quality of tri-exponential IVIM, we developed an unsupervised physics-informed deep neural network (IVIM 3 -NET). We assessed its performance in simulations and in patients with non-alcoholic fatty liver disease (NAFLD) and compared outcomes with bi-exponential LSQ and NN fits and tri-exponential LSQ fits. Scanning was performed using a 3.0T free-breathing multi-slice diffusion-weighted single-shot echo-planar imaging sequence with 18 b-values. Images were analysed for visual quality, comparing the bi- and tri-exponential IVIM models for LSQ fits and NN fits using parameter-map signal-to-noise ratios (SNR) and adjusted R 2 . IVIM parameters were compared to histological fibrosis, disease activity and steatosis grades. Parameter map quality improved with bi- and tri-exponential NN approaches, with a significant increase in average parameter-map SNR from 3.38 to 5.59 and 2.45 to 4.01 for bi- and tri-exponential LSQ and NN models respectively. In 33 out of 36 patients, the tri-exponential model exhibited higher adjusted R 2 values than the bi-exponential model. Correlating IVIM data to liver histology showed that the bi- and tri-exponential NN outperformed both LSQ models for the majority of IVIM parameters (10 out of 15 significant correlations). Overall, our results support the use of a tri-exponential IVIM model in NAFLD. We show that the IVIM 3 -NET can be used to improve image quality compared to a tri-exponential LSQ fit and provides promising correlations with histopathology similar to the bi-exponential neural network fit, while generating potentially complementary additional parameters.