the interest is not deductible until the improvements occur is the way I read it.  If you do the cash out refi on Day 1 and don't do the improvments for a year, then for that 1st year, the interest on the cash out is not deductible. 

what is confusing in the publication is it talks about (with examples) what happens if you improve the home first and take the mortgage out later,

but your question is what happens if you take out the mortgage first and do the improvements later - that is simple to me

I couldn't find any Tax Court cases that are on point for OP's original question, but I wonder if Congress really intended this to be open-ended.  For example, what if one waited 10 years to do said improvements?  Could OP then deduct that "extra" amount in year 10 of the refi?

Full disclosure:  The Tax Cuts and Jobs Act of 2017 (“TCJA”) made modifications to the deductibility of home mortgage interest for tax years from January 1, 2018 through December 31, 2025.  Thus, "year 10" in my example might be moot.

@SweetieJean - sure,  why not, but the loan would have amortized in the meantime.

Because the part of the mortgage that amoritizes first is the part that is not aquisition debt or used to substantially improve the home, I wonder if that scheme was Congress's way of limiting the time to improve the home - as the loan amortizes the benefit goes away in any event,. 

example:

1) My mortgage is $300,000 today

2) I do a cash out refi which takes the mortgage balance to $350,000, but do not substantially improve my home...therefore the interest on the $50,000 is not deductible.

3) 10 years from now, the mortgage balance has amoritzed to $320,000 - the interest on the $300,000 is still deductible (because it's the aquisition debt), but interest on the $20,000 is not since it was not aquizition debt and not used to substaintially improve my home/

4) I finally improve my home and spend $30,000 to do that.

5) the entire $320,000 of the mortgage balance is now either aquisition debt or used to substaintially improve my home.  I can deduct all the interest.

There is a whole section in Pub 936 that discusses what happens if you improve your home and THEN do a cash out refi - there are time limits on that.

But there is no additional commentary that I could find on what happens if you cash out first and don't improve the home - other than, it is not deductible, until you improve the home and there is no discussion of a time limit. (but again, the amortization reduces the benefit in any event)

@SweetieJean @NCperson Thank you both very much for your help. That clears it up for me.