Intravoxel incoherent motion magnetic resonance imaging (IVIM-MRI) allows contrast-agent free in vivo perfusion quantification in developing human fetus. However, clinical translation of prenatal IVIM imaging is limited by poor estimation accuracy from low signal-to-noise (SNR) ratio due to strong diffusion encoding, spatial misalignment and dephasing artefacts induced by random fetal motion. To address these issues, we define an implicit signal acquisition model considering non-Gaussian noise and signal dephasing. An artificial neural network is proposed to learn entire posterior of IVIM parameters with this model. This allows uncertainty quantification of the inferred parameters, which we validate with true posterior approximated by Bayesian sampling. Together with a registration-based motion correction pipeline, the proposed method is evaluated on in vivo fetal MR images. Compared to the conventional least squares (LSQ) approach, this approach achieves higher estimation accuracy on synthetic data and increases repeatability of parameter estimation in placenta for the in vivo cases.