As a title, “Beginners” sounds a note of humility, albeit self-consciously — does that make it a little arch? Certainly it’s the right name for writer-director Mike Mills’ touchingly autobiographical new film, in which a commitment-phobic graphic artist is supportive but bewildered when his father comes out of the closet at 75, just in time to face a terminal illness.

A role model for young creatives of the life-into-art school, Mills stages his own grief as a grappling match between intuition and cleverness. His movie is transparently what most movies are in stealth: an emotional course of decisions. The most useful is the casting. Ewan McGregor and Christopher Plummer, plausibly related, radiate subtle tenderness as the aforementioned son and father, with Mélanie Laurent and Goran Visnjic enlivening slightly underwritten roles as their respective love interests (whose shared essential quality seems to be the convenience of emotional availability). Together, they all look glamorous and movieishly attractive.

The central courtship transpires against an evocative backdrop of hotel rooms, used bookstores, taco trucks and moody Southern California sunlight, with slideshow and graffiti accents. Sometimes it’s hard to know if Mills is old-fashioned and trying to be hip or the other way around, and accrodingly hard to concentrate on anything else. As in his first film, the glassy coming-of-age snapshot “Thumbsucker,” Mills reflexively reaches for his CD-cover and music-video bags of tricks, accumulating indie quirk and risking a veneer of breadth at the expense of depth.

“Beginners” does get a little fidgety flashing back and forward in time and cycling through its arty concepts. Having learned that our hero has tended to let his promising relationships go, we see faux-naif cartoon renderings of his ex-girlfriends; having learned that his father’s tumor is the size of a quarter, we see a screen full of coins. And then there is the matter of the soulful Jack Russell terrier who talks, through subtitles. (One feels uneasy yet duty-bound to point out that Mills is married to Miranda July, whose new movie “The Future” also is in theaters now, and also involves an anguished young creative person, a generation gap, and a talking pet.)

But gradually these mannerisms come to seem less about showing off than about laying bare an authentic, affecting introspection. It recalls not the shallow clutter of recent Michel Gondry but the maturely tragicomic profundity of mid-vintage Woody Allen, deftly transposed into the milieu of a media-saturated generation whose good fortune, Mills’ protagonist confesses, “allowed us to feel a sadness our parents didn’t have time for.” McGregor’s sensitivity is particularly well deployed here, and Mills’ identification is palpable.

Mills’ peculiar but not unproductive course of decisions is a piling up of ornamental textures, so as to better perceive the durable surface of feeling beneath them. Watching this gently assured and open-hearted film gives an unshakable sense that its maker is on his way toward a masterpiece.