"Consumers are making a shift in perception that dairy-free is healthy," Bailey said. "But there's no evidence to prove it."

Part of the issue is that some consumers have eschewed milk for health reasons, said Tom Bailey, the Rabobank analyst who wrote the report.

Those alternatives are still a small slice — just 3 percent of the $600 billion global dairy industry — but they are growing. Dairy alternatives increased 4 percent in the five years ended in 2017, while sales of fluid milk dropped 3.5 percent, according to a recent report by Dutch bank Rabobank.

Consumers are shying away from milk, turning instead to dairy alternatives made from soy, rice and oats, and other crops.

Dairy alternatives companies, he said, have been adept at marketing their products, using clear labeling, touting locally sourced ingredients. Milk's packaging, though, has changed little over the past decade and details of its content are similarly obscure.

"The dairy industry rightfully points to the nutritional and flavor superiority of dairy compared to plant-based beverages," said Bailey. "[But] the makers of dairy alternatives generally appear to be doing a better job of connecting emotionally with consumers who favor more dairy-free options to meet their own perceptions about health and lifestyle."

"How do our products love you back?" Califia Farms, which makes dairy-free probiotic yogurts, creamers and cold-brew coffees, asks on its website. "They love your body by being natural and GMO-free. They love your planet by being sustainably-sourced."

Similar language and goals are shared by Califia Farms' competitors. Those include Ripple, which makes dairy-free pea milk and a "Greek yogurt alternative," and NadaMoo, which makes nondairy coconut ice cream. There's even Perfect Day, which uses yeast and fermentation to make animal-free "milk."

Still, some traditional milk brands have been able to grow.

Coca-Cola, under pressure to reinvent its own drink portfolio as sales of its flagship soda face changing consumer tides, has seen success with its premium milk brand, Fairlife. It touts the high-end milk drink as having the attributes consumers are flocking to: more protein and calcium, less sugar and lactose.

"There's value to be realized in innovation and premiumizing milk products," said Bailey.

Other milk companies could follow suit, he said: They could focus on new packaging or label transparency about where they are sourcing their milk from.

Still, there remains consumer suspicion around products that companies make in mass and about how the animals that provide those products are treated.

Meanwhile, dairy companies could also continue their investment in the space, looking to buy what they cannot create on their own.

Danone acquired WhiteWave, maker of Silk-branded soy milk, for roughly $10 billion in 2017. General Mills has invested in nut yogurt and cheese company Kite Hill.

Correction: This story has been revised to indicate that Ripple's dairy-free milk is made from peas.