Diablo III certainly is taking many elements from its predecessors, but it appears that its health restoration system isn't one of them. Blizzard has put up a handy guide detailing how they have changed everything about how players get health back in Diablo III.
Potions in Diablo III will not be a primary source of healing that can be easily acquired and relied upon. Instead, potions will be uncommon and be set on a cooldown timer. You won't have many of them and you won't be able to use more than one at a time, so they only be useful for emergency healing. Also, while several classes will have abilities that can be used to heal, these will be difficult to use and situational.
Instead of potions or class abilities, players can recover their characters' health by collecting "health globes" that are dropped by defeated enemies. Weak enemies will randomly drop weak health globes when they are slain. Stronger enemies might drop a more powerful health globe when they take a certain amount of damage. Whenever a character collects a health globe, the entire party will regain a set percentage of their health. With this system, Blizzard hopes to strengthen the game's focus on tactical decisions in the midst of combat and pull the focus away from inventory management or needless complexity.