Disclaimer: I’m not a medical professional, nor a psychotherapist, just someone who struggles with normal everyday functioning and in the rare moments when I find something helpful I share with others 

My life has been distilled down to the bare necessities (eating a minimal amount of food, going to a job where I can barely make any progress, avoiding relatives and old friends, I guess you can call it depression, but there is a lack of hopelessness, only a feeling of living in a limbo and mental, physical weakness and emotional numbness. As I was procrastinating shaving my beard, cleaning my apartment, making a amount of food and doing the laundry. I popped in 2 mgs of Clonazepam to sleep away the afternoon. The sleep ended after only an hour, so I decided to shave my beard, vacuum and eat (the laundry I did before). During the whole ordeal I felt sluggish and sleepy, but something made me do those things. 

I believe it would be logical to think that when you’re depressed, you don’t want to engage in anything because you’re sick of the lifeless manner in which you do them and you get negative feedback mental notes which give rise to anxiety about the future. “How will you survive if you struggle with even simple things like this”? Benzodiazepines, or downers in general take away this focus on the future. So when you do something under the influence of these substances, as badly as always (you don’t become more functional), you don’t project the consequences into the future, so you actually get things done with good results. It takes away the future worry based on possible scenarios, all of which you would probably fail, based on your condition and history, so you can just focus on the task.

Maybe this is what makes benzos and anti-anxiety medications so appealing, not only for managing anxiety but for depression also. Keep in mind that anyone’s problems with depression, anxiety or other issues can take many forms and probably are on a spectrum. 

TL;DR: Depression, being debilitating, makes you anxious about taking on responsibilities and tasks.

Anti-anxiety meds help on the short-term, by obfuscating the possible negative outcomes in engaging in tasks while being depressed.