The dependency only goes the other way. If the price of Bitcoin goes up, more people will find it profitable to mine and the difficulty will go up. An equilibrium will be reached as the rising difficulty drives marginal miners out of business.

If new ASICs come out, people start investing in new ASICs instead of other types of mining equipment. Also, people who previously found it unprofitable to mine will start mining. The difficulty will go up. As the difficulty goes up, marginal miners who no longer find it profitable to mine will stop mining. The higher difficulty will drive away potential new miners.

There's no argument I know of that says an increasing difficulty that wasn't itself caused by a higher price would lead to a higher price.

Three things drive up price:

1) Speculation -- people buy Bitcoins in the belief that they will increase in value. This drives up the price as buyers compete for the limited supply. The increase in price encourages more speculation.

2) Demand for a means of exchange -- people buy Bitcoins to use in trade. If the trade volume goes up, that means more Bitcoins are needed to keep the exchange moving.

3) Demand for a store of value -- people buy Bitcoins to hold as a long-term store of value. This doesn't require them to believe they'll go up in value, only that the risk that they will decrease in value is acceptable.