How fine is the line between a volatile temper and full-blown mental illness? That question is at the heart of “Silver Linings Playbook,” David O. Russell’s latest entertaining ode to lovable characters you should probably be afraid of.

Several people are, in fact, afraid of Pat Solatano (Bradley Cooper), who has just been released from a psychiatric hospital after viciously attacking his wife’s lover. Armed with a bipolar diagnosis and a determinedly positive attitude, Pat moves in with his parents (Robert De Niro and Jacki Weaver) and tries to get his old life back.

Of course, it’s not that easy. As his therapist (Anupam Kher) keeps reminding him, Pat does not have a real strategy for self-improvement. He can’t let go of his failed marriage and is oblivious to how much he has damaged his other relationships. He’s also reluctant to take the medications that seem to be the only means of moderating his outbursts.

Things start to improve when he meets Tiffany (Jennifer Lawrence), a young widow whose own emotional damage nearly matches his. They make quite a pair, as they argue and push each other toward a semblance of recovery. She even persuades him to participate in a dance competition, an odd plot twist that turns out to be surprisingly charming.

That’s a good way to describe the whole movie. This is hardly traditional romantic comedy territory, but Russell (adapting Matthew Quick’s 2008 novel) somehow infuses gallows humor with genuine warmth. This pertains not only to the dynamic between Pat and Tiffany, but also to Pat’s interactions with his family, especially his dad. Pat Sr. has his own problems (including a temper), but he’s a loving man who doesn’t know how to help his son. It’s the best role De Niro’s had in years.

It’s no surprise to see Lawrence do great work with a difficult character, but if you only know Cooper from his “Hangover”-esque efforts, prepare for a revelation. The energy he brings to all those slick comedies transfers remarkably well to Pat’s manic desperation.

He gets an assist from Russell’s dynamic, almost jittery direction, which reflects how Pat experiences the world without sending the audience running to the psych ward. That’s no small accomplishment, but the man who made “The Fighter” and “Flirting With Disaster” can certainly pull it off.

In fact, it’s hard to imagine another director so unflinching while remaining so funny and humane. It’s no wonder Russell and his cast are already getting Oscar buzz.

The desire for a Hollywood ending eventually takes over, softening some of the rough edges that make “Silver Linings Playbook” so unique. It’s a noticeable flaw, but not a fatal one. If Russell wants to give his characters a little sugar to help the Seroquel go down, he earns that right, because he makes them earn it, too.

Rated R for language and some sexual content/nudity. At the Barrywoods, Glenwood Arts, Independence, Studio 30 and Town Center.