I have been switching from statsd + graphite + grafana to using influxdb instead of graphite. However somehow InfluxDB behaves a bit differently than graphite used to when it comes to missing values.
If a timeseries does not produce new points for a period of time, the plot in Grafana will continue to show the last value written:

This happens even when specifying fill(0) or fill(null) in the query. When using the Data Interface of InfluxDB it also seems to be filling using the previous values:

Since I have some alerting that will be triggered by missing values, having the old values reused disables my alerts.
Any idea on how to fix this?