It depends on the type of downdraft ... they're not all the same, nor caused by the same types of currents. The most "famous" ones, in terms of recorded incidents are probably on Palancar Wall in Cozumel. These are like submerged waterfalls, and tend to push you down the face of a wall. As DD stated above, if you can swim far enough away from the wall you can generally get out of them. The risk, of course, is that they're not as localized as you think they are (and you can't really tell), and it pushes you into the abyss as you try getting away from it. I'd think a less risky approach would be to swim "into" the wall and find something to hang onto or even to pull yourself up. Currents tend to decrease when you get very close to structure, and in any case hanging on won't make you go any deeper. These currents are usually transient, and in a few minutes can disappear altogether. And if you're holding onto something you won't be working so hard, and therefore not sucking through your air so fast. Yes, I know it violates a basic "no touch" principle ... but diving's a situational activity, and in situations like this you have to sometimes "break the rules" in order to survive. Prioritize your risks.
At my local mudhole we have a well-known phenomenon known as the "Redondo River". It's a strong transient current ... usually occurs during periods of a large ebb ... that can pull you downslope at times. A few years back we lost a diver when she tried swimming upslope in the current and ran herself out of air. Again, a better approach is to get low to the bottom and if possible find something to hang onto until it passes ... usually only takes a few minutes. Or you can try swimming parallel to it (crabbing), but if you guess wrong and swim the wrong way you'll only be tracking with the current as it moves down the beach. I've experienced this current many times, and often there are several minutes of "warning" as the current goes from mild to wild. If you're aware of the building current you can use that time to get yourself shallower or find some structure to duck behind to get out of it. The key is to put yourself into a situation where you don't have to work hard and therefore suck through your air too quickly.
The other option is to swim upward, filling your BCD as needed to gain enough buoyancy to overcome the pull of the downwelling. This is risky, and you really have to pay attention so you don't become a cork when you do break free of the current ... it's something I'd consider a last option. The best approach is to hang on and wait it out, paying attention to your available air supply so you don't run yourself out of gas before you run out of options.
... Bob (Grateful Diver)