BEIJING (AP) -- President Donald Trump's hopes for China's help with restraining North Korea appear to have gone nowhere, with the sides growing further apart as their approaches and concerns diverge.
 
China shows no sign of caving to US pressure to tighten the screws on Pyongyang, while the North's recent missile tests have done little to rattle Beijing, in contrast to the anxiety sparked in Washington. China's bottom line continues to hold fast: No to any measures that might topple Kim Jong Un's hard-line communist regime.
 
"There's been a lot of wishful thinking on the US side that China was coming around in its approach," said John Delury, a professor at Yonsei University in Seoul.
 
Trump seemed to think he'd found a partner on North Korea in Chinese President Xi Jinping following their April summit in Florida. Yet, North Korea continued to test missiles and China continued to keep open, and even expand, economic channels with Pyongyang. By this week, the bloom was well and truly off the rose.
 
"Perhaps China will put a heavy move on North Korea and end this nonsense once and for all!" Trump tweeted on Tuesday, as if still holding out for a Hail Mary from Beijing. The next day, he seemed requited to the facts: "Trade between China and North Korea grew almost 40% in the first quarter. So much for China working with us _ but we had to give it a try." 
 
Where persuasion hasn't worked, Trump's administration has turned to threats. Washington's U.N. ambassador Nikki Haley warned Wednesday that China's trade with the US could suffer if it didn't help out following Pyongyang's successful launch of an intercontinental ballistic missile. Haley said that "much of the burden of enforcing U.N. sanctions rests with China," which accounts for 90 percent of trade with North Korea.
 
The US has already blacklisted one Chinese bank accused of illicit dealings with North Korea and is penalizing a Chinese shipping company and two Chinese individuals accused of facilitating illegal activities by the North. US officials say they plan to look at other Chinese entities as possible targets of so-called secondary sanctions.
 
Already on Monday, Xi appeared to respond to the downturn in ties, warning in a phone call with Trump that "some negative factors" were hurting the relationship.
 
Although Beijing is far from happy with the current situation, and relations between Beijing and Pyongyang are getting "colder and colder," China will remain resistant to any approach to Pyongyang other than a multilateral one, especially one that involved the United Nations, said Niu Jun, an expert at Peking University in Beijing.
 
North Korea's missile tests, meanwhile, aren't seen as such a concern because China itself doesn't feel threatened, Niu said. "For China, it's a question of regional imbalance, of contradictions between the sides," Niu said.
 
In keeping with that sense of threat level, China has counseled a calm approach centered on negotiations and bilateral give-and-take. That is seen most prominently in what has become known as the "dual suspension" proposal whereby North Korea suspends its nuclear and missile tests in return for the US and South Korea suspending large-scale military exercises that Pyongyang sees as rehearsal for an invasion.
 
That idea, which originated with Pyongyang, has been rejected by the US and some experts see it as a ploy by Beijing to avoid committing itself. "It requires nothing on China's part, so it's easy for them to make such a proposal," Delury said. 
 
Meanwhile, a fundamental disagreement over the utility of sanctions remains a major obstacle to further cooperation, said Tong Zhao, an associate at the Carnegie-Tsinghua Center for Global Policy, a think tank in Beijing.
 
The US seems to believe that sanctions must be so tough as to threaten the survival of the Pyongyang regime and force them to end their programs. Yet, by leaving Kim feeling even more under threat, ending their programs might be the last thing Pyongyang does, Tong said. "China still doesn't understand the American logic," he said.
 
Despite poor relations between Xi and Kim, China remains heavily invested in the North Korean regime. It acts as a buffer with the South and the 30,000 American troops stationed there, and remains a reliable, if isolated communist ally. Chinese companies benefit from a lack of competition in the North and worries over the Kim regime distract from China's own controversial actions in the South China Sea and elsewhere.
 
The collapse of the regime, on the other hand, would bring a set of unknowns _ civil war, loose nukes, refugees flowing across the Chinese border and US and South Korean troops on the Yalu River _ none of which are particularly appetizing to Beijing.
 
That China sees relatively little reason to act on North Korea is born out also in its concerns that events on the peninsula are overshadowing other aspects of the US-China relationship.
 
"You can't say that they're coming closer on North Korea, but not everything has to do with that," said Shi Yinhong, a professor of international relations at Beijing's Renmin University.
 
"It's not good to have everything else crushed under the issue of North Korea," he said.