Bayesian HMM clustering of x-vector sequences (VBx) has become a widely adopted diarization baseline model in publications and challenges. It uses an HMM to model speaker turns, a generatively trained probabilistic linear discriminant analysis (PLDA) for speaker distribution modeling, and Bayesian inference to estimate the assignment of x-vectors to speakers. This paper presents a new framework for updating the VBx parameters using discriminative training, which directly optimizes a predefined loss. We also propose a new loss that better correlates with the diarization error rate compared to binary cross-entropy — the default choice for diarization end-to-end systems. Proof-of-concept results across three datasets (AMI, CALLHOME, and DIHARD II) demonstrate the method’s capability of automatically finding hyperparameters, achieving comparable performance to those found by extensive grid search, which typically requires additional hyperparameter behavior knowledge. Moreover, we show that discriminative fine-tuning of PLDA can further improve the model’s performance. We release the source code with this publication.