Diatoms are unicellular organisms, and as such, they mostly reproduce asexually. In other protists, that means cellular duplication, but in diatoms things are made slightly more complex by the presence of they frustule. The frustule is the protective shell that diatoms produce from Silica, to protect themselves. Glass-like in structure, frustule cannot simply be « hatched » by the duplicating cell. The trick is in the shape of the frustule. Not always obvious to the untrained eyes, frustules are always formed by two component, one of which is just enough smaller than the other one to be encased in it.
Once the diatom cell is ready to reproduce, the two parts of the frustule separate under pressure of the growing mother cell. Once mitosis* happened, each of the two new cells leaves with one half of the frustule that becomes its bigger half, and goes on to produce a smaller half of their new frustule. After a certain number of reproduction cycles, things become rather awkward for the daughter cell that inherits the smaller part of the frustule. Indeed at each reproductive cycle, the size of the frustule becomes smaller and smaller, until it is far from ideal.
At that point the diatom change its strategy and switch to a sexual reproduction. The cell goes through meiosis** and the resulting gametes*** fertilise and become the brand new diatom that produce a perfectly respectable frustule size.
* a type of cell division that results in two daughter cells each having the same number and kind of chromosomes as the parent
** a type of cell division that results in four daughter cells each with half the number of chromosomes of the parent
***a mature male or female germ cell, with half the parent genetic material, able to unite with another of the opposite sex