The two canvases that were tapped for the installation are both titled “Carousel II” (1968), and each one unfurls at a length of about 75 feet. Which is not to say that they’re twins. The one on the left hews closer to the wall, and has soft-edged bars of color melting into each other with the unapologetic allure of a pink-streaked sunset. The second painting, which stands to the right, is comparatively chaotic and crossed with long lines that were apparently created by folding and creasing a still-wet canvas, a technique that resembles the Japanese craft of shibori, or hand-dyeing. The painting protrudes aggressively into the viewer’s space, and raises a favorite art-historical conundrum: Is it a painting or is it a sculpture?

Another work in the exhibition — the only other one, in fact — might seem to pose a similar question. “Spread,” a large, horizontal, cherry-red abstraction crackling with citrusy oranges and yellows, has poles that tilt across its surface as if to offer a dyed-fabric version of Pollock’s “Blue Poles.” Although “Spread” is not a Drape painting — it stays in place on the wall much the way paintings are supposed to do — it, too, comes with a novel twist. It belongs to Mr. Gilliam’s “Beveled-Edged” series, in which he slants his stretcher bars at a 45-degree angle, making them instantly visible to the viewer and adding an element of bulk or boxiness to the painting.

Is this detail important? An accompanying handout that is intended for the general public can feel a bit academic, emphasizing how Mr. Gilliam’s methods “transition his two-dimensional paintings away from the flatness traditionally associated with the medium and toward three-dimensional space.” He’s presented as a kind of post-Minimalist whose concerns happen to jibe with those of the sculptors collected in depth by Dia. They include Robert Morris, the master of draped industrial felt, and Anne Truitt, who is also from Washington, and whose spare, platonic, monochromatic objects occupy a teasingly ambiguous realm where painting leaves off and sculpture begins.

But Mr. Gilliam himself has not characterized his work in Minimalist or post-Minimalist terms. If anything, he has said that his work derives from more earthy and accidental inspirations. His Drape paintings, he said last month, “might have been inspired by seeing laundry hanging on a clothesline.” He made the comment in an interview with the art historian Barbara Rose, and added, intriguingly, that he could not discount the possible influence of a coterie of artists he had met in Paris in the early ’60s who branded their efforts “sans chassis” — which is French for “off the stretcher.”

At any rate, one wouldn’t want to pin the Drape paintings to a single source. They are richly and dreamily allusive. “Double Merge” has many layers of meaning, and its spirit, however festive at first glance, can also feel mournful. As it hangs down from the ceiling, or rather from wooden slats that attach to points along the top of the canvas that are bunched and tied with brown leather straps, the piece can evoke an unsettling sense of hanging bodies, of lynchings, and the incalculable sorrows of the American past.

“When artists leave the South,” Mr. Gilliam once said to the historian William Ferris, “their southernness takes on guises.”