Yes a big ass capacitor on the 12v Rail of the strip.
a 1N4001 is a multipurpose diode rated up to 100v the 1N4007 is it's 700v version, which is commonly used for rectifier bridges in mains power applications. They are easy to come by handle a fair amount of current and voltage. A 7805 is a 5v regulator which i thought you were using, anyway it looks a lot like the regulator in your drawing. 7805 comes in different packages, but the to-220 package that is in your drawing is the easiest, it handles the current demand of the ESP without any extra heatsink. It may not perform properly without capacitors on the output, but there is one on the D1, and for more stable power supply it is good to have an input capacitor, which you can separate with a diode from the rest of the 12v DC.
I do when i connect it straight to a MCU to protect the output pin. People will argue that it is to protect the strip, but as far as i can tell, the strip has a logical input, and the output should be protected against overcurrent or bounce.
The ledstrip should have the input protected against accidental 12v, cause that does break them.
Which brings me to something i realized after i turned of my laptop last night.
That applies to WS2812B's, which run ideally on 5v. (apparently they can run on something as low as 3.5v but i have yet to try that) 12v strip uses WS2811's which can run at a voltage of 12v as well (and probably something in between) as long as you increase the value of the current limiting resistor, from the 100R for 5v. Check the datasheet (or measure on the strip) for the 12v spec. The WS2811 handles 3 LED's in series at 12v, where for the RED there is another current limiting resistor (less voltage drop on those 3 reds.) Most strips have 2 0 Ohms resistors for the Green & Blue. So i would say the cutoff is really close the 3.3v anyway, and timing is very important.