Are there weapons which regenerate ammo?

In Borderlands 1 I had a great pistol which only had a 2-shot clip but reloaded almost instantly and it also regenerated ammunition over time, fast enough that it basically had infinite ammo. I haven't found a gun in BL2 that has this ability, are there any? I'm playing as Commando and I've noticed Gunzerker class mods that seem to grant this ability, but I was hoping there are weapons that do it too. The need to stop questing and go searching through containers for ammo or find an ammo vending machine is a little annoying.

Weapons that REGENERATE ammo

Note, the following two weapons require a purchase of the Ultimate Vault Hunter Upgrade pack

Avenger

Counterbution revengence. The reckoning. – High overall stats. Behaves like a bouncing betty grenade when reloaded. Regenerates SMG ammo when wielded.

Butcher

Fresh Meat! – Very low pellet count. Greatly increased fire rate. Achieves maximum accuracy much more quickly than other Hyperion shotguns. Magazine randomly refills a random amount of ammo as it's fired, giving it a wildly variable magazine size in use. Fire rate highly increases under sustained fire.

Grenade Mods that REGENERATE ammo

The following 4 mods will require purchase of the DLC, Tiny Tina's Assault on Dragonkeep

Lightning Bolt

What's a jigawatt? – Always Shock. Regenerates grenade ammo over time. Shoots straight forward with a lightning graphic and explodes on impact. Character may shout "Lightning Bolt!" and a custom throwing sound will be heard after use while playing in Tiny Tina's Assault on Dragon Keep.

Chain Lightning

Don't pay it back, pay it forward. – Always Shock. Regenerates grenade ammo over time. Shoots a bolt of lightning straight forward that explodes on impact and arcs to nearby targets. Character may shout "Lightning Bolt!" after use while playing in Tiny Tina's Assault on Dragon Keep.

Fireball

Porkchop Sandwiches! – Always incendiary. Regenerates grenade ammo over time. Shoots a slow moving fireball straight forward that explodes on impact. When used, has a custom sound effect when thrown and the character may shout "fireball!" while in the DLC Tiny Tina's Assault on Dragon Keep.

Fire Storm

What manner of man are you that can summon up fire without flint or tinder? – Always incendiary. Regenerates grenade ammo over time. Shoots a fireball straight forward that explodes on impact. Four additional fireballs spawn above the spot of the original explosion and fall to the ground. Character may shout "Fireball!" upon use while playing in Tiny Tina's Assault on Dragon Keep.

Magic Missile

No wand required. Just point and shoot. – Always slag. Grenades slowly regenerate over time. Two (Blue rarity) or Four (Purple rarity) child grenades home in on targets and explode instantly. Character may shout "Magic Missile!" after use while playing in Tiny Tina's Assault on Dragon Keep.

Weapons that DON'T consume any ammo

Infinity:

It's closer than you think! (no it isn't) – Does not consume ammunition. Shots fired form a fixed lemniscate (∞) pattern, ignoring normal recoil behavior. Increased accuracy when aiming down the sights.

As an extra note, you'll need to have at least 1 bullet of pistol ammo, or the Infinity will not fire.

Some Vladof launchers:

Vladof launchers can have the special ability "reduced ammo consumption," which means that every third shot fired is not deducted from either the magazine or the player's ammo stock. This is coupled with lower base damage, though the overall destructive capacity of the weapon remains roughly the same as an equivalent launcher from most other manufacturers.

Near as I can tell, no there are no guns with ammo regen.

A quick Google search turns up many similar threads, obviously people are missing it from Borderlands 1. Some alternatives:

• Play the Gunzerker. He has class mods for personal and team ammo regen, and the "Gunzerking" class ability, which regenerates ammo for all of his guns (unlocked very early). Gunzerker also has class skills for increasing ammo capacity. Play this guy, and you'll never have an ammo problem (in my experience).
• Apparently certain shields exist which "capture" bullets that are shot at (and hit) you.
• Use Eridium to expand your ammo capacity for your favorite guns.