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Are there grounds to hope the Kashmir dispute can be resolved?

In the years prior to the Mumbai (Bombay) attacks of November 2008 - in which gunmen killed 165 people - relations between India and Pakistan saw a big thaw.
The Mumbai attacks were blamed by India on militants based in Pakistan and led India to suspend further negotiations until February 2010, when the first formal discussions between the two countries since the attacks were held in Delhi.
Before those attacks the two countries agreed on several Kashmir-specific confidence building measures. A bus service between the two parts of Kashmir was resumed in 2005.

In October 2008 an old trade road was reopened after 60 years across the Line of Control (LoC) that divides Indian and Pakistani-administered Kashmir. Earlier in the same month a rail service was introduced.

The two governments have huge international backing to continue the peace process and make their negotiations succeed.
An end to the violence and uncertainty in Kashmir would also be widely welcomed in India and Pakistan - and not only by those weary of the fighting or those who see it as a hindrance to the economic development of the South Asia region.

However, a diplomatic solution has escaped both sides for more than 60 years, and there are no signs of any new proposals yet.
Furthermore, both governments face powerful hard line groups within their own countries who will be carefully monitoring the talks to make sure concessions they deem to be unacceptable are not offered to the other side.