In “Anomalisa,” an inspirational speaker in crisis checks into Cincinnati’s (fictional) Al Fregoli hotel, named for a delusional condition in which paranoiacs believe that those around them are not who they appear to be, but a single tormentor hiding behind multiple disguises. That’s a helpful bit of trivia to consider before entering into Charlie Kaufman’s latest brainteaser, this one originally mounted (just twice) for composer Carter Burwell’s “Theater of the New Ear” sound-play experiment and rescued from obscurity by a team of imaginative producers who thought it might make an interesting stop-motion project — which it does, exceptional even, although it’s unclear just who they imagined might be the audience for such a cerebral cult offering.

“Anomalisa’s” existence is a minor miracle on multiple levels, from the Kickstarter campaign that funded it (the credits give “special thanks” to 1,070 names) to the oh-so-delicate way the film creeps up on you, transitioning from a low-key dark night of the soul into something warm, human and surprisingly tender. This despite the fact that it’s told entirely through puppets — which proved to be plenty expressive in “Being John Malkovich,” the film that put Kaufman on the cinematic map. Now, it’s been seven long years since his directorial debut, “Synecdoche, New York,” and Kaufman owes his return at least in part to co-director Duke Johnson (the “Moral Orel” helmer who oversaw “Community’s” all-stop-motion Christmas episode).

Here, working on a modest budget with limited sets (an airplane, the Al Fregoli and a couple other locations) and just three voice actors, Kaufman recovers creative control of an eccentric little project that ultimately manages to move us as deeply as his more ambitious, format-melting fare. The connection starts with road warrior Michael Stone (voiced by David Thewlis) touching down in Cincinnati, where he’s scheduled to give one of his “How May I Help You to Help Them?” pep talks before hopping on a plane home the following day.

Michael knows his speech inside-out, but for some reason, the words ring hollow tonight. He’s been thinking about leaving his wife; he’s been thinking about Bella, the woman he walked out on 11 years earlier. Bella lives in Cincinnati. After settling into his hotel room (have you ever seen a stop-motion puppet use the loo? or gaze out the window to find a man masturbating in the office park across the way?), he gives Bella a call and invites her over.

Remember the aforementioned Fregoli syndrome — that peculiar ailment whose sufferers believe everybody’s the same person out to get them? (Fregoli also happens to be the pen name Kaufman used when he first unveiled the play in 2005.) There’s a reason why every time Bella opens her mouth, we hear the flat, vaguely monotonous sound of Tom Noonan’s voice. The same thing happens when anybody in “Anomalisa” speaks: Michael’s wife, his son, the taxi driver or hotel concierge — all Noonan. Anybody except Lisa, that is. Her voice (Jennifer Jason Leigh’s) cuts through the din and forces Michael out of his room to find its source.

Where the film had seemed almost listless in its opening act, something clicks when Lisa enters the picture. There’s a liveliness to Leigh’s voice, and it’s reflected in both her body language and her facial expressions, so much as either can be conveyed by these limited-range stop-motion puppets. Michael invites Lisa for a drink, dragging her friend Emily (Noonan again) along to the hotel bar. He wants to bring her back to his room, where he makes an indecent proposal, and she nearly walks out. And then the ice melts, and they connect — over a Cyndi Lauper song, of all things. Watching them, expect to feel an indescribable mix of affinity and loneliness, as only Kaufman can achieve, that same ache that accompanied “Eternal Sunshine of the Spotless Mind” or burned alongside Samantha Morton’s smoldering house in “Synecdoche, New York.”

What follows is both beautiful and heartbreaking, and ultimately unforgettable. Kaufman has done it again, writing a deeply flawed male protagonist and a woman who seems so incredibly ideal despite (or perhaps due to) her imperfections, and he’s engineered it so that we fall in love: Michael’s gray and overcast, Lisa just wants to walk in the sun, and for as long as he can make the moment last, she’s the one. The anomaly. The Anomalisa.

Of course, that feeling, which you never want to end, can’t go on forever. The movie itself is only 90 minutes, and however Joycean may be Kaufman’s postmodern spirit, he doesn’t share ol’ Sunny Jim’s belief in epiphanies. Michael experiences such a breakthrough, or thinks he does, only to have it implode and crumble back into itself in a scene that is so wonderfully Kaufman-esque: a chorus of Noonans offering themselves at Michael’s feet, the death of love, the implied womp womp of a sad-trombone ending (not literally, of course).

In terms of actual music, it’s surprising how little of Burwell’s music features into “Anomalisa,” considering that the play was first staged in concert with a live orchestration. Surely this must be one of the typically melancholy composer’s gentlest scores, tinkling away ever so lightly in the background, subtly lifting the spirit of an otherwise heavy piece — much as Leigh does with her voice.

So much of the experience relies on listening, depending as much on the actors’ intonations as the words themselves. Naturally, the animated format directs our attention to the visual, but it’s best to think of this as a bonus — and, frankly, not to be too particular about the technique. Kaufman and Johnson use a form of face-replacement stop-motion, not unlike that featured (to far more polished effect) by Laika Studios, where the characters’ faces are split into upper and lower halves and switched out for every frame. The expressions themselves — brows and jowls — are generated via color 3D printers, which yield a grainy vaguely flesh-toned series of interchangeable masks.

For some reason (likely budget, though it could also be justified by the film’s self-conscious nature), the directors opted not to erase the joints in post, leaving a conspicuous seam running across the puppets’ faces at all times. By design, Michael’s noggin features more color and detail than all the others, and beneath those baggy doll clothes, they have real rubber bodies, which come in handy for what the MPAA has deemed “graphic nudity” (this being the org that nearly slapped an NC-17 on “Team America” for “graphic crude and sexual humor, violent images and strong language — all involving puppets”).

Working on a fraction of the budget of last year’s po-mo “The Lego Movie,” “Anomalisa” likewise embraces the limitations of its “cast” — although there are other glitches still to be ironed out, including a weird rippling effect that appears across the faces in most scenes. Perhaps the inks weren’t consistent, or maybe slight differences in position between one faceplate and the next bounced the light differently. Whatever the cause, the resulting flicker distracts from what we should be looking at — which is how wonderfully expressive these otherwise rudimentary foot-tall puppets manage to be. As when Wes Anderson dabbled in stop-motion for “Fantastic Mr. Fox,” it’s a strange medium in which to find a perfectionist. But that’s life, which, ironically, Kaufman and company seem to have done a fine job of conjuring in this most artificial of formats.