Are you seeing any output in the Nginx error log? Run:
<pre>
tail -n25 /var/log/nginx/error.log
</pre>

What packages were upgraded?

I had a similar error after php update.

1. Go to /var/run # cd /var/run #sudo chmod 666 php5-fpm.sock 2.Enjoy!

Ran into same problem. I just edited my /etc/php5/fpm/pool.d/www.conf file.

Set

listen.owner = www-data  
listen.group = www-data 
listen.mode = 0660 

Restarted php5-fpm.

Logs showed
2014/06/24 20:04:25 [crit] 2223#0: *10547 connect() to unix:/var/run/php5-fpm.sock failed (13: Permission denied) while connecting to upstream, client: <snip>

Update (Nice we can edit the posts now)

Looking into this more closely it looks like it fixes bug CVE-2014-0185 incorrect socket permissions.

CVE-2014-0185

The default PHP FPM socket permission has been changed from 0666
to 0660 to mitigate a security vulnerability (CVE-2014-0185) in PHP
FPM that allowed any local user to run a PHP code under the active
user of FPM process via crafted FastCGI client.

The default Debian setup now correctly sets the listen.owner and
listen.group to www-data:www-data in default php-fpm.conf.  If you
have more FPM instances or a webserver not running under www-data
user you need to adjust the configuration of FPM pools in
/etc/php5/fpm/pool.d/ so the accessing process has rights to
access the socket.