For a 16-bit ADC to be useful you need things like really quiet power supplies, really accurate and stable voltage references, ground planes, and a whole lot of calibration. So a lot of times it's a bit pointless to use a 16-bit ADC. Did you just pick it because it was the highest resolution you could find? Most 16-bit ADCs aren't even accurate to 16-bits (so a 14-bit ADC might do just the same and be able to sample faster too). If you used a 12-bit ADC it would sample even faster. It takes quite a lot to squeeze out the full accuracy of a 16-bit ADC.
What are you using it for? Do you even need 16-bits? Do you even need a clamping diode and a current limiting resistor at the input? Because at 16-bits you want to add as little as possible since everything will introduce noise.
And what makes you think most of the noise is coming from the diode? If it's clamping it's probably connected between input and +V right? I would think most of the noise comes from the resistor sitting in series with the input.