If and when the talks do convene, United Nations mediators will have to overcome a huge chasm between the rival sides to secure the concrete steps they seek at Hodeida docks and Sanaa airport. The Saudi-led coalition went to war with the rebels the following March.
Saudi Arabia is unlikely to tolerate what it views as an Iranian proxy on its doorstep, and the Houthis have little incentive to withdraw from the capital and other territories they have captured and held at great cost.
With no decisive military victory for either side in sight, the war has ratcheted up enormous humanitarian costs.
"Aside from who started the war and who has committed war crimes, because war crimes have been committed, Yemen is nearly back to the middle ages".
"Now it is up to you, the Yemini parties", she said.
The US State Department hailed the peace talks in Sweden as a "necessary and vital first step" and called on all parties to "cease any ongoing hostilities".
Although no date has been announced for the start of the negotiations, Yemeni government sources say they could begin on Thursday.
Houthi rebels have said they will attend if they are guaranteed safe passage.
His arrival coincided with the evacuation of a number of wounded Houthis from the capital to Muscat, Oman.
A delegation from Yemen's internationally recognised government is expected to arrive in Sweden on Wednesday, a Yemeni official told The National.
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Kuwait's Deputy Foreign Minister Khaled al-Jarallah earlier told reporters that his country's ambassador to Yemen would also accompany the rebel delegation travelling to Stockholm.
A number of Western countries, the U.S. and Britain in particular, are also accused of being complicit in the ongoing aggression as they supply the Riyadh regime with advanced weapons and military equipment as well as logistical and intelligence assistance.
An agreement to exchange hundreds of detainees was welcomed by the International Committee of the Red Cross, which will oversee the swap after the first round of planned peace talks in Sweden.
The mounting humanitarian needs, and outrage over the killing of Saudi writer Jamal Khashoggi, have galvanized global support for ending the war.
On Tuesday, as Griffiths and the Houthis were making their way to Stockholm, Sweden was preparing to receive the delegation from the Hadi regime. The government delegation and the head of the rebel delegation travelled to Sweden on Wednesday. The Hadi regime is hoping for a political settlement under which the Houthis recognise its "legitimacy" while the Houthis are more focused on easing humanitarian conditions.
The proposed UN-brokered peace talks have been backed by both the rebels and the Saudi-led government and were expected to take place in Sweden this week.
"It's not much, but given the humanitarian situation and toxic political atmosphere now prevalent in Yemen, it's better than nothing".
Regional diplomats are no less sceptical.
The UN considers Yemen the world's worst humanitarian crisis, and has repeatedly warned of a looming starvation.