New York (CNN) In his first speech before the United Nations, President Donald Trump stood before the hall's iconic green marble wall and deployed for the first time in person his infamous moniker aimed at North Korea's leader Kim Jong Un.

A year later, as he prepares to deliver his second UN speech on Tuesday, the US President has almost entirely abandoned his fiery, bellicose rhetoric in favor of trumpeting his personal diplomatic efforts to resolve the North Korean nuclear crisis and expressing a hearty optimism. He has retired the "Rocket Man" moniker -- and its "Little Rocket Man" variation -- since last winter and has even promised to deliver a CD with the eponymous Elton John song to Kim.

That the cutting insult has achieved inside joke status between the two leaders exemplifies the extent of the diplomatic détente between the US and North Korea in the year since Trump delivered those jarring threats at the UN and its lightning-fast pace. In that span of time, Trump and Kim turned from exchanging a menacing volley of insults and threats of annihilation to meeting face-to-face in Singapore , showering each other with praise and making broad commitments to ending a decades-old war footing.

North Korea has tested neither a nuclear weapon nor a ballistic missile in 10 months; North Korea has resumed an effort to return the remains of American soldiers from the Korean War to the US ; and Kim and South Korean President Moon Jae-in have hit one diplomatic milestone after another in recent months.

"There is no denying that there's been huge changes in one year," said Joseph Yun, who served as the US's special representative for North Korea policy until February. "If someone had told you 12 months ago, 'Would you take stopping nuclear tests, stopping missile tests, getting some remains of American soldiers back and all that stuff?' Of course you would take it, in a heartbeat."

"It was unimaginable then. The most likely outcome September last year was a kind of 'bloody nose,'" he said, referring to considerations of a preventive US strike.

'No concrete indications'

The reduced tensions, however, are where the rosy portrait of the Trump administration's diplomatic endeavor ends.

"As of yet," Yun said, "there are no concrete indications that Kim Jong Un has genuinely shown signs of being committed to denuclearization."

Despite multiple promises to do so since Trump and Kim's June summit, North Korea has yet to take any concrete, verifiable and irreversible steps toward denuclearization -- conditions laid out by the US State Department. Instead, North Korea has resisted US requests for a list declaring the extent of its nuclear weapons facilities and weapons and is continuing to enrich nuclear material and build nuclear weapons -- it now simply does so quietly, with little public fanfare.

The dichotomy between the rosy public optics and the reality that North Korea is continuing to advance its nuclear weapons program, unabated, has widened the gap between how Trump and his top aides on the matter are approaching the next steps in the United States' diplomatic endeavor and its odds of success.

Despite the lack of concrete progress, Trump has pressed aides in recent weeks to organize a second summit with Kim, a US official and source familiar with the deliberations said, sticking to the belief that his personal touch can lead the two countries to a breakthrough. He added immediacy to his desire for a second summit on Monday as he arrived at UN headquarters, declaring that he and Kim will hold a second summit "quite soon."

"It looks like we'll have a second summit quite soon. As you know, Kim Jong Un wrote a letter -- a beautiful letter -- and asked me for a second meeting and we will be doing that. Secretary Pompeo will work that out in the immediate future," Trump said, claiming there has been "tremendous progress on North Korea."

'This is a different world'

Mindful of the optics, the President also contrasted the state of affairs a year after his menacing words on North Korea a year ago at the UN: "This is a different world. That was a very dangerous time. This is one year later, a much different time."

The President's advisers on North Korea, meanwhile, have sought to delay convening a second summit, focusing instead on pressing the North Koreans to agree to demonstrate a serious commitment toward denuclearization.

Chief among the US team's demands, one source familiar with the negotiations said, remains the request for a North Korean declaration of its nuclear facilities and arsenal. US officials are now also considering pressing North Korea to follow through on Kim's commitment to Moon this month to shut down its Yongbyon nuclear facility and allow inspectors in as a first step before a second summit, the source said.

Secretary of State Mike Pompeo, who has remained the administration's point person on North Korea, is expected to meet with a North Korean counterpart on the sidelines of this week's UN General Assembly, with a second summit one of the main agenda points.

Trump, meanwhile, will meet with Moon and Japanese Prime Minister Shinzo Abe on the sidelines of the annual UN meetings here. Moon has been an enthusiastic advocate for talks between Trump and Kim. Abe has been more cautious, advocating an approach that doesn't let up sanctions pressure on a country that's fired test missiles over his country.

Even amid hardening intelligence showing North Korea's nuclear program continuing apace, the President has insisted that another face-to-face could help convince Kim to take more concrete steps toward denuclearization. Casting the effort as a sales job that he alone will be able to close, he has openly hailed the kinship with Kim developed during a first summit in Singapore and has told his team he's spent a lifetime developing relationships that he can turn into successful transactions, a US official said.

Some American officials, meanwhile, have privately expressed concern that a second meeting could confer approval on a regime that has taken few steps toward the goal of denuclearization, the sources said. As with Trump's first meeting, aides wonder what concessions Trump may offer Kim in private, including the potential end of the Korean War, a step long sought by North Korea that US officials believe must come only in exchange for more solid steps toward denuclearization.

Trump's eagerness to meet again with Kim is matched only by the North Korean leader, who has repeatedly telegraphed his desire for a second summit with Trump.

Forging ahead

In the months leading up to and succeeding the Singapore summit, Kim has watched as the international pressure campaign mounted by the United States has slowly cracked. The US has continued to enforce sanctions with the same verve, but China has loosened some of its enforcement of the internationally imposed economic pressure on North Korea. South Korea has forged ahead with strengthening inter-Korean ties notwithstanding its neighbor's lack of concrete steps toward denuclearization.

In perhaps Kim's most significant victory from the summit, Trump pledged after the summit to suspend major US-South Korean military exercises.

"On the whole, the maximum pressure campaign was effective and did play some role in getting the North Koreans to the table," said Michael Green, a former Bush administration official and the senior vice president for Asia at the Center for Strategic and International Studies. "But the President himself was so excited about the summitry (in Singapore), that the pressure dissipated ... Trump gave it all away in Singapore and more."

"North Korea is behaving somewhat better and that's clear, but back in their caves and facilities, the CIA has made it very clear publicly that they continue to build the most dangerous nuclear weapons and ballistic missiles that concerned us in the first place. And nothing they've put on the table addresses that," he added.

Now, Trump could soon face the choice between reneging on the public pledges he made early in his presidency to never allow North Korea to obtain the capability to strike the US with a nuclear weapon and accepting North Korea as a quiet nuclear power that must perpetually be deterred from using its weapons.

North Korea, experts say, appears to be using the diplomatic détente to achieve the latter outcome. And as of now, it's not clear which direction Trump will go.

"There is a degree of disconnect between how the (President's) senior staff see the path to a nuclear deal and how the North Koreans see the path," Yun, the former US special representative, said. "Whether the President sides with the path of his senior staff or the path of the North Koreans seems to me at the moment -- I don't know, he could go either way."