Diplotene
The correct stage during which separation of the paired homologous chromosomes begins is the diplotene stage. This stage is a sub-phase of meiosis, specifically occurring during the first meiotic division.

Explanation:

1. Diplotene Stage:
- The diplotene stage is characterized by the separation of the paired homologous chromosomes, which were initially paired during the preceding prophase I stages (leptotene, zygotene, and pachytene).
- During diplotene, the homologous chromosomes begin to move apart but are still connected at points called chiasmata, where genetic recombination has occurred.
- This stage allows for the exchange of genetic material between homologous chromosomes, leading to genetic diversity in the resulting gametes.

Comparison with Other Prophase I Stages:
- Leptotene: The chromosomes start to condense.
- Zygotene: Homologous chromosomes begin to pair up.
- Pachytene: Pairing of homologous chromosomes is complete, and crossing over occurs.
- Diakinesis: Chromosomes condense further, and the nuclear envelope breaks down.

Significance:
- The separation of homologous chromosomes during diplotene is crucial for ensuring that each resulting gamete receives a unique combination of genetic material.
- This genetic diversity is essential for evolution and adaptation in sexually reproducing organisms.
In conclusion, the diplotene stage of meiosis is where the separation of paired homologous chromosomes begins, setting the stage for the subsequent events in meiotic division.