#Java 10, (削除) 100 (削除ここまで) 106 bytes

b->{var s="";int i=0,j;for(var c:b){if(c)for(s+="\n",j=i;j-->0;)s+=0;else++i;s+=1;}return s.substring(1);}

Takes an array of booleans and returns a String (0s are empty, 1s are filled). Try it online here.

Thanks to Olivier Grégoire for helping me golf it a bit more and alerting me to the fact that my output format was not up to the spec.

Ungolfed version:

b -> { // lambda taking an array of booleans as argument
 var s = ""; // the output String
 int i = 0, // the number of "empty" characters to output
 j; // iterator variable for outputting the "empty" characters
 for(var c : b) { // iterate over the boolean array (the binary digits)
 if(c) // if it's a '1'
 for(s += "\n", // output a newline
 j = i; j-- > 0;) s += 0; // output the "empty" characters
 else // if it's a '0'
 ++i; // move one to the right on the next line
 s += 1; // output the "filled" character
 }
 return s.substring(1); // output the constructed String, minus the leading newline
}

Java 10, (削除) 100 (削除ここまで) 106 bytes

b->{var s="";int i=0,j;for(var c:b){if(c)for(s+="\n",j=i;j-->0;)s+=0;else++i;s+=1;}return s.substring(1);}

Takes an array of booleans and returns a String (0s are empty, 1s are filled). Try it online here.

Thanks to Olivier Grégoire for helping me golf it a bit more and alerting me to the fact that my output format was not up to the spec.

Ungolfed version:

b -> { // lambda taking an array of booleans as argument
 var s = ""; // the output String
 int i = 0, // the number of "empty" characters to output
 j; // iterator variable for outputting the "empty" characters
 for(var c : b) { // iterate over the boolean array (the binary digits)
 if(c) // if it's a '1'
 for(s += "\n", // output a newline
 j = i; j-- > 0;) s += 0; // output the "empty" characters
 else // if it's a '0'
 ++i; // move one to the right on the next line
 s += 1; // output the "filled" character
 }
 return s.substring(1); // output the constructed String, minus the leading newline
}

#Java 10, (削除) 100 (削除ここまで) 106 bytes

b->{var s="";int i=0,j;for(var c:b){if(c)for(s+="\n",j=i;j-->0;)s+=0;else++i;s+=1;}return s.substring(1);}

Takes an array of booleans and returns a String (0s are empty, 1s are filled). Try it online here.

Thanks to Olivier Grégoire for helping me golf it a bit more and alerting me to the fact that my output format was not up to the spec.

Ungolfed version:

b -> { // lambda taking an array of booleans as argument
 var s = ""; // the output String
 int i = 0, // the number of "empty" characters to output
 j; // iterator variable for outputting the "empty" characters
 for(var c : b) { // iterate over the boolean array (the binary digits)
 if(c) // if it's a '1'
 for(s += "\n", // output a newline
 j=i; j-->0;) s+=0; // output the "empty" characters
 else // if it's a '0'
 ++i; // move one to the right on the next line
 s+=1; // output the "filled" character
 }
 return s.substring(1); // output the constructed String, minus the leading newline
}

#Java 10, (削除) 100 (削除ここまで) 106 bytes

b->{var s="";int i=0,j;for(var c:b){if(c)for(s+="\n",j=i;j-->0;)s+=0;else++i;s+=1;}return s.substring(1);}

Takes an array of booleans and returns a String (0s are empty, 1s are filled). Try it online here.

Thanks to Olivier Grégoire for helping me golf it a bit more and alerting me to the fact that my output format was not up to the spec.

Ungolfed version:

b -> { // lambda taking an array of booleans as argument
 var s = ""; // the output String
 int i = 0, // the number of "empty" characters to output
 j; // iterator variable for outputting the "empty" characters
 for(var c : b) { // iterate over the boolean array (the binary digits)
 if(c) // if it's a '1'
 for(s += "\n", // output a newline
 j = i; j-- > 0;) s += 0; // output the "empty" characters
 else // if it's a '0'
 ++i; // move one to the right on the next line
 s += 1; // output the "filled" character
 }
 return s.substring(1); // output the constructed String, minus the leading newline
}

#Java 10, 100 bytes

b->{var s="";int i=0,j;for(var c:b)if(c){s+="\n";for(j=i;j-->0;)s+=0;s+=1;}else{i++;s+=1;}return s;}

Takes an array of booleans and returns a String (0s are empty, 1s are filled). Try it online here.

Ungolfed version:

b -> { // lambda taking an array of booleans as argument
 var s = ""; // the output String
 int i = 0, // the number of "empty" characters to output
 j; // iterator variable for outputting the "empty" characters
 for(var c : b) // iterate over the boolean array (the binary digits)
 if(c) { // if it's a '1'
 s += "\n"; // output a newline
 for(j = i; j-- > 0; ) // output the "empty" characters
 s += 0;
  s+=1; // output the "filled" character
 } else { // if it's a '0'
 i++; // move one to the right on the next line
 s+=1; // output the "filled" character
 }
 return s; // output the constructed String
}

#Java 10, (削除) 100 (削除ここまで) 106 bytes

b->{var s="";int i=0,j;for(var c:b){if(c)for(s+="\n",j=i;j-->0;)s+=0;else++i;s+=1;}return s.substring(1);}

Takes an array of booleans and returns a String (0s are empty, 1s are filled). Try it online here.

Thanks to Olivier Grégoire for helping me golf it a bit more and alerting me to the fact that my output format was not up to the spec.

Ungolfed version:

b -> { // lambda taking an array of booleans as argument
 var s = ""; // the output String
 int i = 0, // the number of "empty" characters to output
 j; // iterator variable for outputting the "empty" characters
 for(var c : b) { // iterate over the boolean array (the binary digits)
 if(c) // if it's a '1'
 for(s += "\n", // output a newline
 j=i; j-->0;) s+=0; // output the "empty" characters
 else // if it's a '0'
 ++i; // move one to the right on the next line
 s+=1; // output the "filled" character
 }
 return s.substring(1); // output the constructed String, minus the leading newline
}