Lumintop Ant Man (14500 LEP flashlight)

A simple buck boost driver could be like this :

Monomode, capable of 2A output at 4Vout (likely too much for the module used in the Ant Man, here it’s set at 1A), no thermal regulation (no MCU), but it does have LVP thanks to the R1/R2 divider on the Enable pin. We could do without the 2.5V voltage reference by connecting R3 to VOUT, but the current will be quite approximate due to the Vf variation, the LDO used for the VREF is quite cheap anyway.
By some miracle this BB converter is still in stock at Mouser and is actually slightly better than the one used in the lume1 driver.

With this it should still have a soft start at startup, the issue with the constant current topology I’m using in my other drivers is that it has the tendency to spike at startup, which apparently isn’t good for laser diodes.

For a more powerfull driver for driving a LEP module like this:

I would do something different since commonly available BB converter are not powerfull enough for 3A@4V, I would use a boost converter with a constant voltage output >= Vf and use a constant current linear regulation after that, since the Vf will be high even in thermal step-down the efficiency should remain good. A boost converter with passthrough would be used so that it just outputs Vin when Vin>Vout (e.g. when the battery is full).
The soft start function would also work properly in this case.