Senior negotiator Sofyan Djalil told reporters as he arrived in Helsinki on Monday that he was extremely optimistic.
"Hopefully Tuesday's round can solve all the problems and hopefully by August we can sign the final [deal]," he said.
And rebel spokesman Tengku Kafrawi said both sides had nothing to lose because accepting some form of autonomy while remaining part of Indonesia was an acceptable compromise.
"We are looking at a win-win solution … if a decision is taken by our leaders we will accept it. We are ready to lay down our arms if our leaders make that decision."
Note of caution
Observers, however, remained cautious about the prospect for peace, mindful of earlier failed attempts and the risk that unruly rebel and military factions will try to scupper the process.
"I am optimistic that the negotiations will be able to bring peace to Aceh, but only if the two sides are really committed to ending the conflict and upholding the people's interests," leading Aceh rights activist Rufriadi Ramli said.
And chief mediator of the talks, former Finnish President Martti Ahtisaari, also sounded a more cautious note.
"The parties agreed to let [the mediators] work on the drafts of the agreements, which we submitted two weeks ago," he told journalists. "We have heard nothing from either side since then."
Topics for discussion
The talks, due to start on Tuesday and last for five days, are seen as decisive because they will tackle the most intractable outstanding issues, such as giving a political role to the Free Aceh Movement and the demilitarisation of the province of 4.1 million people.
The Aceh conflict has raged since 1976 and has killed at least 15,000 people. Peace efforts collapsed in 2003, but were revived after the 26 December earthquake and tsunami that left more than 130,000 dead in the province.
Former Finnish President Martti
Ahtisaari is chairing the talks
Since the disaster, the two sides have met four times in Helsinki under the auspices of the Crisis Management Initiative, a conflict prevention group set up by Ahtisaari after he stepped down as Finland's president in 2000.
Jakarta has said it will never let Aceh separate from Indonesia, but will give it a greater say in running its affairs.
Sensitive election issue
The rebels have publicly dropped their independence demand, and now want the right to form their own regional political party to take part in elections for the provincial government.
This party issue is sensitive for Jakarta, because it is generally expected that the separatists would overwhelmingly win any free vote.
Rebel spokesman Bachtiar Abd Allah said the only way to a comprehensive peace was "through a negotiated agreement that gives to the people of Aceh the right and capacity to determine their own affairs within the context of the Republic of Indonesia".
Ahtisaari warned that the peace process would not be able to move forward without agreement on all outstanding issues.
"Nothing is agreed until everything is agreed," Ahtisaari said.