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TORONTO — Ask people in Canada what they make of American health care, and the answer typically falls between bewilderment and outrage.

Canada, after all, prides itself on a health system that guarantees government insurance for everyone. And many Canadians find it baffling that there’s anybody in the United States who can’t afford a visit to the doctor.

So even as Canadians throw shade at the American hodgepodge of public plans, private insurance, deductibles and copays, they hold in high esteem a little-known Affordable Care Act initiative: the federal Center for Medicare & Medicaid Innovation (CMMI).

It was a hot topic on a reporter’s recent visit to Toronto to study the single-payer health care system.

Wonky as it seems, the center’s mission — testing innovations to hold down health care costs while increasing quality — has gotten noticed. Researchers and clinicians talk about its potential to foster experimentation and how it has led the United States to think out of the box regarding payment and reimbursement models.

“It is gaining traction in many circles here,” said Robert Reid, who researches health care quality at the University of Toronto.

“There have been some good efforts … they have tried more things than we have,” agreed Dr. Kaveh Shojania, a Toronto-based internist who studies health care quality and safety.

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Despite the praise emanating from north of the border, the program doesn’t get the same love on the homefront.

Through the ACA, CMMI is armed with $10 billion each decade and sponsors on-the-ground experiments with doctors, health systems and payers. The idea is to devise and implement payment approaches that reward health care quality and efficiency, rather than the number of procedures performed.

Since taking office, though, President Donald Trump has rolled back its reach.

Canada has its own reasons for seeing potential in this sort of systemic test kitchen.

Health care’s growing price tag — and a payment system that doesn’t necessarily reward keeping people healthy — is hardly just an American problem. The vast majority of Canadian doctors are paid through what Americans call the “fee-for-service” model. And Canadian policymakers are also looking for strategies to curb health care costs — which, while greater in the United States, are a big budget here, too.

“The whole world is confronting the same issue, which is, ‘How do you pay and incentivize doctors to keep people out of the hospital and keep them healthy?’” said Ezekiel Emanuel, a former adviser to President Barack Obama who pushed for the center’s initial development. “Different places are looking at how to break out of that system, because everyone knows its perversions. This is one place where … we are in the world among the most innovative groups.”

Emanuel added that he wasn’t surprised to hear of the center’s appeal in Canada. He has received similar feedback from health ministers in Belgium and France, he said.

Even so, U.S. critics say CMMI’s work is a waste of money or a federal overreach.

And, so far, the Trump administration has reduced by half the size of one high-profile Obama administration project that would have bundled payments for hip and knee replacements — so that the hospitals performing those were paid a set amount, rather than for individual services. It also canceled other scheduled “bundling” projects targeting payment for cardiac care and other joint replacements.

CMS Administrator Seema Verma wrote in The Wall Street Journal in September that the Innovation Center was going to begin moving “in a new direction.”

A follow-up “request for information” from the federal government suggested that the center would emphasize cutting health care costs through strategies like market competition, eliminating fraud and helping consumers actually shop for care. It also suggested the Innovation Center would favor smaller-scale projects.

At least for now, it’s hard to interpret what this means, said Jack Hoadley, a health policy analyst at Georgetown University who has previously worked at the Department of Health and Human Services.

Limiting CMMI’s footprint would be problematic, Emanuel argued, while discussing CMMI’s status in the U.S.

The footprint in Canada, though, seems to be growing.

“We definitely looked to it as a model as something we can do. Like look, this happened, and why can’t we do the same thing here?” said Dr. Tara Kiran, a Toronto-based primary care doctor who also researches health care quality.