'assiduate' originates from Latin, specifically the adjective 'assiduus', where 'ad-' meant 'to' (or 'toward') and 'sedēre' meant 'to sit', giving the sense of 'being continually present'.

'assiduus' in Latin led to Late Latin/Medieval Latin formations such as 'assiduare' (to make continual or to be constant), and this eventually yielded the rare English formation 'assiduate' in modern usage.

Initially it carried the idea of 'being continually present or seated (persisting)', and over time it evolved into the current sense of 'paying continual, diligent attention' or 'being persistent/diligent'.