Infinitely vs Deeply - What's the difference?

As adverbs the difference between infinitely and deeply

is that infinitely is in an infinite manner; as of anything growing without bounds; endlessly while deeply is at depth, in a deep way.

(en adverb)

in an infinite manner; as of anything growing without bounds; endlessly

To a surpassingly large extent.

(en-adv)

At depth, in a deep way.

To a deep extent.

profoundly

* deep (adverb sense )