Bdtyktl

From 5.1 onwards you can't install according to what @Martin mentioned.
Download libcudnn6_6.0.21-1+cuda8.0_amd64.deb, libcudnn6-dev_6.0.21-1+cuda8.0_amd64.deb, libcudnn6-doc_6.0.21-1+cuda8.0_amd64.deb from nvidia site and install one by one follwing way.

 sudo dpkg -i <library_name>.deb

1. Register on NVidia's website. It may take a day, or two before they'll get your account approved. At least that used to be the case back when I registered.


2. 
   

   Download and Install latest CUDA from NVidia, or the latest version that fits the software you'll be working with, if any, in this case your version of T-Flow.

   
   
   

   Note, that installing via ubuntu's standard package manager via clicking probably won't work appropriately.

   
   
   

   Instead, you'll probably have to follow these instructions in the terminal to install .deb pakage. After that you'll have to add a few lines to .bashrc, or wherever appropriate in your case. For example, if you're configuring a server, it's probably going to be a different place, maybe somewhere prior to your app's autolaunch, as .bashrc will probably not get executed in that case.

   
   


3. 
   

   Download CuDNN from NVidia

   
   
   

   I used the "Library for Linux" version, didn't have much luck with .deb packages.

   
   



4. You can find where CUDA is located via
   which nvcc. Usually /usr/local/cuda/ will be a symbolic link to your currently installed version.



5. Open CuDNN archive and copy appropriate contents into appropriate places within CUDA installation folder (cuda/lib64/ and cuda/include/). I usually sudo nautilus and do it from there visually.

Fast forward 2018 and NVIDIA now provides cuDNN 7.x for download. The installation steps are still similar with those described by @GPrathap. But if you want to replace the old cuDNN version with the newer one, you need to remove it first prior to the installation.

To recap:

Step 0. Verify that you already have installed CUDA toolkit. Proceed with CUDA toolkit installation if you haven't.

Step 1. Go to NVIDIA developer portal https://developer.nvidia.com/cudnn and download cuDNN.

Step 2. If you have previously installed cuDNN, remove it

sudo dpkg -r <old-cudnn-runtime>.deb

sudo dpkg -r <old-cudnn-dev>.deb

Step 3. Install the cuDNN library (runtime, dev, doc) using dpkg

sudo dpkg -i <new-cudnn-runtime>.deb

sudo dpkg -i <new-cudnn-dev>.deb

sudo ldconfig

Step 4. If you want to find where the library was installed you can update the locate index and then find the library location.

sudo updatedb

locate libcudnn

If you are specifically installing cuDNN 7.x against CUDA toolkit 9.1, this article provides more elaboration that can be of some help: http://tech.amikelive.com/node-679/quick-tip-installing-cuda-deep-neural-network-7-cudnn-7-x-library-for-cuda-toolkit-9-1-on-ubuntu-16-04/

Also, you can download the deb packages for Debian based distributions.

From the NVIDIA web page, for the developer profile are available the next files :

• cuDNN v5.1 Runtime Library for Linux (Deb)


• cuDNN v5.1 Developer Library for Linux (Deb)


• cuDNN v5.1 Code Samples and User Guide Linux (Deb)

I tested this, over my machine with Debian (Stretch) and TensorFlow is working !

Adding an important detail to the still valid answers by @Martin Thoma and @Íhor Mé:
After copying the libcudnn files to the cuda directories, you must update your .bashrc file:

export LD_LIBRARY_PATH="$LD_LIBRARY_PATH:/usr/local/cuda/lib64:/usr/local/cuda/extras/CUPTI/lib64"

export CUDA_HOME=/usr/local/cuda

You must then add the include directory to any config file that uses it.
Caffe e.g. has a config file which you must edit before compiling with make. For this, edit caffe/Makefile.config to add the paths to these config variables(add whitespace between paths):

INCLUDE_DIRS: /usr/local/caffe/cuda/include/ 

LIBRARY_DIRS: /usr/local/cuda/lib64/

For every current terminal window you want these changes to be effective, don't forget to execute the file once!

. ~/.bashrc

the answer is correct but for cuDNN 5.1 some names have been changed. So if you use this version after extracting the cuDNN file you will find two folder: lib and include. change the name of *.h file in include folder to cudnn.h and then follow https://askubuntu.com/a/767270/641589. this change is needed if you wanted to use cuDNN for Caffe!

In 16.04 if you are installing CUDA directly from Nvidia's website and you are also building Tensorflow from source then you can specificy the directory you want to indicate as being Cudnn. By default it is :

/usr/include/x86_64-linux-gnu

When you are building Tensorflow it will ask you which version you want to indicate you are using for Cudnn. Then after that it will ask where is it located. Just indicate the directory above and it will work fine. It should create a wheel file at that point and you can install it with pip.