"Today's assumption" or "todays assumption" — which is valid grammar?
The apostrophe indicates possession.
Without an apostrophe you are indicating plurality.
Since the point you are trying to convey is that the assumption you made yesterday is no longer valid, the apostrophe is appropriate.
Yesterday's assumption is no longer valid.
It's kind of like saying "The assumption of yesterday".
It's absolutely necessary, to show that you mean of yesterday. The alternative, plural of yesterday, is rare but does exist : "All our yesterdays have lighted fools/ the way to dusty death", Macbeth.