We propose Sortformer, a novel neural model for speaker diarization, trained with unconventional objectives compared to existing end-to-end diarization models. The permutation problem in speaker diarization has long been regarded as a critical challenge. Most prior end-to-end diarization systems employ permutation invariant loss (PIL), which optimizes for the permutation that yields the lowest error. In contrast, we introduce Sort Loss, which enables a diarization model to autonomously resolve permutation, with or without PIL. We demonstrate that combining Sort Loss and PIL achieves performance competitive with state-of-the-art end-to-end diarization models trained exclusively with PIL. Crucially, we present a streamlined multispeaker ASR architecture that leverages Sortformer as a speaker supervision model, embedding speaker label estimation within the ASR encoder state using a sinusoidal kernel function. This approach resolves the speaker permutation problem through sorted objectives, effectively bridging speaker-label timestamps and speaker tokens. In our experiments, we show that the proposed multispeaker ASR architecture, enhanced with speaker supervision, improves performance via adapter techniques. Code and trained models will be made publicly available via the NVIDIA NeMo framework